Publicacions Matemàtiques Articles (Project Euclid)

The $K$-Group of Substitutional Systems

Thu, 05 Aug 2010 15:41 EDT

Aziz El Kacimi, Rajagopalan Parthasarathy

Source: Publ. Mat., Volume 54, Number 1, 3--23.

Abstract:
In another article we associated a dynamical system to a non-properly ordered Bratteli diagram. In this article we describe how to compute the $K$-group $K_0$ of the dynamical system in terms of the Bratteli diagram. In the case of properly ordered Bratteli diagrams this description coincides with what is already known, namely the so-called dimension group of the Bratteli diagram. The new group defined here is more relevant for non-properly ordered Bratteli diagrams. We use our main result to describe $K_0$ of a substitutional system.

Thu, 05 Aug 2010 15:41 EDT

Brett D. Wick

Source: Publ. Mat., Volume 54, Number 1, 25--52.

Abstract:
It is shown that for $H^\infty_\mathbb{R}(\mathbb{D})$ functions $f_1$ and~$f_2$ with $\inf_{z\in\mathbb{D}}(\vert f_1(z)\vert+\vert f_2(z)\vert)\geq\delta>0$ and $f_1$ being positive on the real zeros of $f_2$, then there exists $H^\infty_\mathbb{R}(\mathbb{D})$ functions $g_2$ and~$g_1$, $g_1^{-1}$ with norm controlled by a constant depending only on $\delta$ and $g_1f_1+g_2f_2=1\quad\forall\; z\in\mathbb{D}$. These results are connected to the computation of the stable rank of the algebra $H^\infty_\mathbb{R}(\mathbb{D})$ and to results in Control Theory.

A Boundedness Criterion for General Maximal Operators

Thu, 05 Aug 2010 15:41 EDT

Andrei K. Lerner, Sheldy Ombrosi

Source: Publ. Mat., Volume 54, Number 1, 53--71.

Abstract:
We consider maximal operators $M_{\mathcal B}$ with respect to a basis ${\mathcal B}$. In the case when $M_{\mathcal B}$ satisfies a reversed weak type inequality, we obtain a boundedness criterion for $M_{\mathcal B}$ on an arbitrary quasi-Banach function space $X$. Being applied to specific ${\mathcal B}$ and $X$ this criterion yields new and short proofs of a number of well-known results. Our principal application is related to an open problem on the boundedness of the two-dimensional one-sided maximal function $M^{+}$ on $L^p_w$.

$f$-Polynomials, $h$-Polynomials, and $l^2$-Euler Characteristics

Thu, 05 Aug 2010 15:41 EDT

Dan Boros

Source: Publ. Mat., Volume 54, Number 1, 73--81.

Abstract:
We introduce a many-variable version of the $f$-polynomial and $h$-polynomial associated to a finite simplicial complex. In this context the $h$-polynomial is actually a rational function. We establish connections with the $l^2$-Euler characteristic of right-angled buildings. When $L$ is a triangulation of a sphere we obtain a new formula for the $l^2$-Euler characteristic.

Thu, 05 Aug 2010 15:41 EDT

J. F. Jardine

Source: Publ. Mat., Volume 54, Number 1, 83--111.

Abstract:
Gerbes are locally connected presheaves of groupoids on a small Grothendieck site $\mathcal{C}$. They are classified up to local weak equivalence by path components of a cocycle category taking values in the big $2$-groupoid $\mathbf{Iso}(\Gr(\mathcal{C}))$ consisting of all sheaves of groups on $\mathcal{C}$, their isomorphisms and homotopies. If $\mathcal{F}$ is a full subpresheaf of $\mathbf{Iso}(\Gr(\mathcal{C}))$ then the set $[\ast,B\mathcal{F}]$ of morphisms in the homotopy category of simplicial presheaves classifies gerbes locally weakly equivalent to objects of $\mathcal{F}$. If $\St(\pi \mathcal{F})$ is the stack completion of the fundamental groupoid $\pi\mathcal{F}$ of $\mathcal{F}$, if $L$ is a global section of $\St(\pi\mathcal{F})$, and if $F_{L}$ is the homotopy fibre over $L$ of the canonical map $B\mathcal{F} \to B\St(\pi\mathcal{F})$, then $[\ast,F_{L}]$ is in bijective correspondence with Giraud's non-abelian cohomology object $H^{2}(\mathcal{C},L)$ of equivalence classes of gerbes with band $L$.

Joining Polynomial and Exponential Combinatorics for Some Entire Maps

Thu, 05 Aug 2010 15:41 EDT

Antonio Garijo, Xavier Jarque, Mónica Moreno Rocha

Source: Publ. Mat., Volume 54, Number 1, 113--136.

Abstract:
We consider families of entire transcendental maps given by $F_{\lambda,m} (z) = \lambda z^m \exp(z) $ where $m \ge 2$. All these maps have a superattracting fixed point at $z=0$ and a free critical point at~$z=-m$. In parameter planes we focus on the capture zones, i.e., we consider $\lambda$ values for which the free critical point belongs to the basin of attraction of $z=0$. We explain the connection between the dynamics near zero and the dynamics near infinity at the boundary of the immediate basin of attraction of the origin, thus, joining together exponential and polynomial behaviors in the same dynamical plane.

Algebraic Webs Invariant under Endomorphisms

Thu, 05 Aug 2010 15:41 EDT

Marius Dabija, Mattias Jonsson

Source: Publ. Mat., Volume 54, Number 1, 137--148.

Abstract:
We classify noninvertible, holomorphic selfmaps of the projective plane that preserve an algebraic web. In doing so, we obtain interesting examples of critically finite maps.

On the Sum Product Estimates and Two Variables Expanders

Thu, 05 Aug 2010 15:41 EDT

Chun-Yen Shen

Source: Publ. Mat., Volume 54, Number 1, 149--157.

Abstract:
Let ${\mathbb F}_p$ be the finite field of a prime order~$p$. Let $F \colon {\mathbb F}_p \times {\mathbb F}_p\rightarrow {\mathbb F}_p$ be a function defined by $F(x,y)=x(f(x)+by)$, where $b \in {\mathbb F}_p^*$ and $f\colon {\mathbb F}_p \rightarrow {\mathbb F}_p$ is any function. We prove that if $A \subset {\mathbb F}_p$ and $|A|<p^{1/2}$ then $|A+A|+|F(A,A)| \gtrapprox |A|^{\frac{13}{12}}.$ Taking $f=0$ and $b=1$, we get the well-known sum-product theorem by Bourgain, Katz and Tao, and Bourgain, Glibichuk and Konyagin, and also improve the previous known exponent from $\frac{14}{13}$ to $\frac{13}{12}$.

Some Remarks About Parametrizations of Intrinsic Regular Surfaces in the Heisenberg Group

Thu, 05 Aug 2010 15:41 EDT

Francesco Bigolin, Davide Vittone

Source: Publ. Mat., Volume 54, Number 1, 159--172.

Abstract:
We prove that, in general, ${\mathbb H}$-regular surfaces in the Heisenberg group $\mathbb{H}^1$ are not bi-Lipschitz equivalent to the plane ${\mathbb R}^2$ endowed with the ``parabolic'' distance, which instead is the model space for $C^1$ surfaces without characteristic points. In Heisenberg groups $\mathbb{H}^n$, ${\mathbb H}$-regular surfaces can be seen as intrinsic graphs: we show that such parametrizations do not belong to Sobolev classes of metric-space valued maps.

Index of an Implicit Differential Equation

Thu, 05 Aug 2010 15:41 EDT

L. S. Challapa, M. A. S. Ruas

Source: Publ. Mat., Volume 54, Number 1, 173--186.

Abstract:
In this paper we introduce the concept of the index of an implicit differential equation $F(x,y,p)=0,$ where $F$ is a smooth function, $p=\frac{dy}{dx}$, $F_{p}=0$ and $F_{pp}=0$ at an isolated singular point. We also apply the results to study the geometry of surfaces in $\mathbb{R}^{5}$.

Integration with respect to local time and Itô's formula for smooth nondegenerate martingales

Thu, 05 Aug 2010 15:41 EDT

Xavier Bardina, Carles Rovira

Source: Publ. Mat., Volume 54, Number 1, 187--208.

Abstract:
We show an Itô's formula for nondegenerate Brownian martingales $X_t=\int_0^t u_s \,dW_s$ and functions $F(x,t)$ with locally integrable derivatives in $t$ and $x$. We prove that one can express the additional term in Itô's s formula as an integral over space and time with respect to local time.

Thu, 05 Aug 2010 15:41 EDT

Ramūnas Garunkštis, Antanas Laurinčikas, Kohji Matsumoto, Jörn Steuding, Rasa Steuding

Source: Publ. Mat., Volume 54, Number 1, 209--219.

Abstract:
We apply an effective multidimensional $\Omega$ result of Voronin in order to obtain effective universality-type theorems for the Riemann zeta-function. We further use this approach to study approximation properties of linear combinations of derivatives of the zeta-function.

Thu, 05 Aug 2010 15:41 EDT

Jorge J. Betancor, Juan C. Fariña, Lourdes Rodríguez-Mesa, Ricardo Testoni, José L. Torrea

Source: Publ. Mat., Volume 54, Number 1, 221--242.

Abstract:
We discuss two possible definitions for Sobolev spaces associated with ultraspherical expansions. These definitions depend on the notion of higher order derivative. We show that in order to have an isomorphism between Sobolev and potential spaces, the higher order derivatives to be considered are not the iteration of the first order derivatives. Some discussions about higher order Riesz transforms are involved. Also we prove that the maximal operator for the Poisson integral in the ultraspherical setting is bounded on the Sobolev spaces.

Sur les Automorphismes Réguliers de $\mathbb{C}^k$

Thu, 05 Aug 2010 15:41 EDT

Henry de Thélin

Source: Publ. Mat., Volume 54, Number 1, 243--262.

Abstract:
We show the uniqueness for the measure of maximal entropy for regular automorphisms of $\mathbb{C}^k$.

Okutsu-Montes representations of prime ideals of one-dimensional integral closures

Wed, 22 Jun 2011 09:22 EDT

Enric Nart

Source: Publ. Mat., Volume 55, Number 2, 261--294.

Abstract:
This is a survey on Okutsu-Montes representations of prime ideals of certain one-dimensional integral closures. These representa- tions facilitate the computational resolution of several arithmetic tasks concerning prime ideals of global fields.

Exceptional singularities of codimension one holomorphic foliations

Wed, 22 Jun 2011 09:22 EDT

Marco Brunella, Carlo Perrone

Source: Publ. Mat., Volume 55, Number 2, 295--312.

Abstract:
We study some numerical properties of singularities of codimension one holomorphic foliations which can be analytically collapsed to one point. Some local and global dynamical consequences are deduced.

Conical square functions and non-tangential maximal functions with respect to the gaussian measure

Wed, 22 Jun 2011 09:22 EDT

Jan Maas, Jan van Neerven, Pierre Portal

Source: Publ. Mat., Volume 55, Number 2, 313--341.

Abstract:
We study, in $L^{1}({\mathbb R}^n;\gamma)$ with respect to the gaussian measure, non-tangential maximal functions and conical square functions associated with the Ornstein-Uhlenbeck operator by developing a set of techniques which allow us, to some extent, to compensate for the non-doubling character of the gaussian measure. The main result asserts that conical square functions can be controlled in $L^1$\guio{norm} by non-tangential maximal functions. Along the way we prove a change of aperture result for the latter. This complements recent results on gaussian Hardy spaces due to Mauceri and Meda.

Rational inner functions in the Schur-Agler class of the polydisk

Wed, 22 Jun 2011 09:22 EDT

Greg Knese

Source: Publ. Mat., Volume 55, Number 2, 343--357.

Abstract:
Every two-variable rational inner function on the bidisk has a spe- cial representation called a unitary transfer function realization. It is well known and related to important ideas in operator theory that this does not extend to three or more variables on the poly- disk. We study the class of rational inner functions on the poly- disk which do possess a unitary realization (the Schur-Agler class) and investigate minimality in their representations. Schur-Agler class rational inner functions in three or more variables cannot be represented in a way that is as minimal as two variables might suggest.

Series parallel linkages

Wed, 22 Jun 2011 09:22 EDT

James Cruickshank, Jonathan McLaughlin

Source: Publ. Mat., Volume 55, Number 2, 359--378.

Abstract:
We study spaces of realisations of linkages (weighted graphs) whose underlying graph is a series parallel graph. In particular, we describe an algorithm for determining whether or not such spaces are connected.

Polynomial differential equations with many real ovals in the same algebraic complex solution

Wed, 22 Jun 2011 09:22 EDT

A. Lins Neto

Source: Publ. Mat., Volume 55, Number 2, 379--399.

Abstract:
Let $\operatorname{Fol}_{\mathbb{R}}(2,d)$ be the space of real algebraic foliations of degree $d$ in $\mathbb{R} \mathbb{P}(2)$. For fixed $d$, let $\operatorname{Int}_{\mathbb{R}}(2,d)=\lbrace\mathcal{F}\in \operatorname{Fol}_{\mathbb{R}}(2,d)\mid \mathcal{F}$ has a non-constant rational first integral$\rbrace$. Given $\mathcal{F}\in \operatorname{Int}_\mathbb{R}(2,d)$, with primitive first integral~$G$, set $O(\mathcal{F})=$ number of real ovals of the generic level $(G=c)$. Let $O(d)=\sup\lbrace O(\mathcal{F})\mid \mathcal{F}\in \operatorname{Int}_{\mathbb{R}}(2,d)\rbrace$. The main purpose of this paper is to prove that $O(d)=+\infty$ for all $d\ge5$.

Embedded curves and foliations

Wed, 22 Jun 2011 09:22 EDT

Hossein Movasati, Paulo Sad

Source: Publ. Mat., Volume 55, Number 2, 401--411.

Abstract:
We prove the existence of regular foliations with a prescribed tangency divisor in neighborhoods of negatively embedded holomorphic curves; this is related to a linearization theorem due to Grauert. We give also examples of neighborhoods which can not be linearized.

A stability result for nonlinear Neumann problems in Reifenberg flat domains in $\mathbb{R}^N$

Wed, 22 Jun 2011 09:22 EDT

Antoine Lemenant, Emmanouil Milakis

Source: Publ. Mat., Volume 55, Number 2, 413--432.

Metric properties of Outer Space

Wed, 22 Jun 2011 09:22 EDT

Stefano Francaviglia, Armando Martino

Source: Publ. Mat., Volume 55, Number 2, 433--473.

Abstract:
We define metrics on Culler-Vogtmann space, which are an analogue of the Thurston metric and are constructed using stretching factors. In fact the metrics we study are related, one being a symmetrised version of the other. We investigate the basic properties of these metrics, showing the advantages and pathologies of both choices. We show how to compute stretching factors between marked metric graphs in an easy way and we discuss the behaviour of stretching factors under iterations of automorphisms. We study metric properties of folding paths, showing that they are geodesic for the non-symmetric metric and, if they do not enter the thin part of Outer Space, quasi-geodesic for the symmetric metric.

Weighted inequalities for multivariable dyadic para-products

Wed, 22 Jun 2011 09:22 EDT

Daewon Chung

Source: Publ. Mat., Volume 55, Number 2, 475--499.

Abstract:
Using Wilson's Haar basis in $\mathbb{R}^n$, which is different than the usual tensor product Haar functions, we define its associated dyadic paraproduct in $\mathbb{R}^n$. We can then extend "trivially'' Beznosova's Bellman function proof of the linear bound in $L^2(w)$ with respect to $[w]_{A_2}$ for the 1-dimensional dyadic paraproduct. Here trivial means that each piece of the argument that had a Bellman function proof has an $n$-dimensional counterpart that holds with the same Bellman function. The lemma that allows for this painless extension we call the good Bellman function Lemma. Furthermore the argument allows to obtain dimensionless bounds in the anisotropic case.

Bilinear Littlewood-Paley for circle and transference

Wed, 22 Jun 2011 09:22 EDT

Parasar Mohanty, Saurabh Shrivastava

Source: Publ. Mat., Volume 55, Number 2, 501--519.

Abstract:
In this paper we have obtained the boundedness of bilinear Littlewood-Paley operators on the circle group ${\mathbb T}$ by using appropriate transference techniques. In particular, bilinear analogue of Carleson's Littlewood-Paley result for all possible indices has been obtained. Also, we prove some bilinear analogues of de Leeuw's results concerning multipliers of ${\mathbb R}^n$.

A mi-chemin entre analyse complexe et superanalyse

Thu, 15 Dec 2011 13:16 EST

Pierre Bonneau, Anne Cumenge

Source: Publ. Mat., Volume 56, Number 1, 3--40.

Abstract:
In the framework of superanalysis we get a functions theory close to complex analysis, under a suitable condition $(A)$ on the real superalgebras in consideration (this condition is a generalization of the classical relation $1 + i^2 = 0$ in $\mathbb{C}$). Under the condition $(A)$, we get an integral representation formula for the superdifferentiable functions. We deduce properties of the superdifferentiable functions: analyticity, a result of separated superdifferentiability, a Liouville theorem and a continuation theorem of Hartogs-Bochner type.

A geometric and stochastic proof of the twist point theorem

Thu, 15 Dec 2011 13:16 EST

Michael D. O'Neill

Source: Publ. Mat., Volume 56, Number 1, 41--63.

Abstract:
In this paper we will give a proof of the McMillan twist point theorem using geometry, potential theory and Ito's formula but not the Riemann mapping theorem.

Isolated singularities of binary differential equations of degree $n$

Thu, 15 Dec 2011 13:16 EST

T. Fukui, J. J. Nuño-Ballesteros

Source: Publ. Mat., Volume 56, Number 1, 65--89.

Abstract:
We study isolated singularities of binary differential equations of degree $n$ which are totally real. This means that at any regular point, the associated algebraic equation of degree $n$ has exactly $n$ different real roots (this generalizes the so called positive quadratic differential forms when $n=2$). We introduce the concept of index for isolated singularities and generalize Poincaré-Hopf theorem and Bendixson formula. Moreover, we give a classification of phase portraits of the $n$-web around a generic singular point. We show that there are only three types, which generalize the Darbouxian umbilics $D_1$, $D_2$ and $D_3$.

An inner automorphism is only an inner automorphism, but an inner endomorphism can be something strange

Thu, 15 Dec 2011 13:16 EST

George M. Bergman

Source: Publ. Mat., Volume 56, Number 1, 91--126.

Abstract:
The inner automorphisms of a group $G$ can be characterized within the category of groups without reference to group elements: they are precisely those automorphisms of $G$ that can be extended, in a functorial manner, to all groups $H$ given with homomorphisms $G\to H.$ (Precise statement in {S.group}.) The group of such extended systems of automorphisms, unlike the group of inner automorphisms of $G$ itself, is always isomorphic to $G.$ A similar characterization holds for inner automorphisms of an associative algebra $R$ over a field $K;$ here the group of functorial systems of automorphisms is isomorphic to the group of units of $R$ modulo the units of $K.$ If one looks at the above functorial extendibility property for endomorphisms, rather than just automorphisms, then in the group case, the only additional example is the trivial endomorphism; but in the $K$-algebra case, a construction unfamiliar to ring theorists, but known to functional analysts, also arises. Systems of endomorphisms with the same functoriality property are examined in some other categories; other uses of the phrase "inner endomorphism'' in the literature, some overlapping the one introduced here, are noted; the concept of an inner derivation of an associative or Lie algebra is looked at from the same point of view, and the dual concept of a "co-inner'' endomorphism is briefly examined. Several open questions are noted.

Thu, 15 Dec 2011 13:16 EST

Viêt-Anh Nguyên

Source: Publ. Mat., Volume 56, Number 1, 127--146.

Abstract:
We construct a canonical Green current $T_f$ for every quasi-algebraically stable meromorphic self-map $f$ of $\mathbb{P}^k$ such that its first dynamical degree $\lambda_1(f)$ is a simple root of its characteristic polynomial and that $\lambda_1(f)>1.$ We establish a functional equation for $T_f$ and show that the support of $T_f$ is contained in the Julia set, which is thus non empty.

Thu, 15 Dec 2011 13:16 EST

David Cruz-Uribe, Kabe Moen

Source: Publ. Mat., Volume 56, Number 1, 147--190.

Abstract:
We prove several sharp weighted norm inequalities for commutators of classical operators in harmonic analysis. We find sufficient $A_p$-bump conditions on pairs of weights $(u,v)$ such that $[b,T]$, $b\in \mathit{BMO}$ and $T$ a singular integral operator (such as the Hilbert or Riesz transforms), maps $L^p(v)$ into $L^p(u)$. Because of the added degree of singularity, the commutators require a "double log bump" as opposed to that of singular integrals, which only require single log bumps. For the fractional integral operator $I_\alpha$ we find the sharp one-weight bound on $[b,I_\alpha]$, $b\in \mathit{BMO}$, in terms of the $A_{p,q}$ constant of the weight. We also prove sharp two-weight bounds for $[b,I_\alpha]$ analogous to those of singular integrals. We prove two-weight weak type inequalities for $[b,T]$ and $[b,I_\alpha]$ for pairs of factored weights. Finally we construct several examples showing our bounds are sharp.

Boundary values in range spaces of co-analytic truncated Toeplitz operators

Thu, 15 Dec 2011 13:16 EST

Andreas Hartmann, William T. Ross

Source: Publ. Mat., Volume 56, Number 1, 191--223.

Abstract:
Functions in backward shift invariant subspaces have nice analytic continuation properties outside the spectrum of the inner function defining the space. Inside the spectrum of the inner function, Ahern and Clark showed that under some distribution condition on the zeros and the singular measure of the inner function, it is possible to obtain non-tangential boundary values of every function in the backward shift invariant subspace as well as for their derivatives up to a certain order. Here we will investigate, at least when the inner function is a Blaschke product, the non-tangential boundary values of the functions of the backward shift invariant subspace after having applied a co-analytic (truncated) Toeplitz operator. There appears to be a smoothing effect.

Asymptotics for the minimum Riesz energy and best-packing on sets of finite packing premeasure

Thu, 15 Dec 2011 13:16 EST

Sergiy Borodachov

Source: Publ. Mat., Volume 56, Number 1, 225--254.

Abstract:
We show that for every compact set $A\subset {\mathbb R}^m$ of finite $\alpha$-dimensional packing premeasure $0<\alpha\leq m$, the lower limit of the normalized discrete minimum Riesz $s$-energy ($s>\alpha$) coincides with the outer measure of $A$ constructed from this limit by method I. The asymptotic behavior of the discrete minimum energy on compact subsets of a self-similar set $K$ satisfying the open set condition is also studied for $s$ greater than the Hausdorff dimension of $K$. In addition, similar problems are studied for the best-packing radius.

Some non-amenable groups

Thu, 15 Dec 2011 13:16 EST

Aditi Kar, Graham A. Niblo

Source: Publ. Mat., Volume 56, Number 1, 255--259.

Abstract:
We generalise a result of R. Thomas to establish the non-vanishing of the first $\ell^2$ Betti number for a class of finitely generated groups.

Boundedness of rough integral operators on Triebel-Lizorkin spaces

Tue, 19 Jun 2012 13:43 EDT

H. M. Al-Qassem, L. C. Cheng, Y. Pan

Source: Publ. Mat., Volume 56, Number 2, 261--277.

Abstract:
We prove the boundedness of several classes of rough integral operators on Triebel-Lizorkin spaces. Our results represent improvements as well as natural extensions of many previously known results.

On $D(-1)$-Quadruples

Tue, 19 Jun 2012 13:43 EDT

Nicolae Ciprian Bonciocat, Mihai Cipu, Maurice Mignotte

Source: Publ. Mat., Volume 56, Number 2, 279--304.

Abstract:
Quadruples $(a,b,c,d)$ of positive integers $a<b<c<d$ with the property that the product of any two of them is one more than a perfect square are studied. Improved lower and upper bounds for the entries $b$ and $c$ are established. As an application of these results, a bound for the number of such quadruples is obtained.

Thompson's group $T$ is the orientation-preserving automorphism group of a cellular complex

Tue, 19 Jun 2012 13:43 EDT

Ariadna Fossas, Maxime Nguyen

Source: Publ. Mat., Volume 56, Number 2, 305--326.

Abstract:
We consider a planar surface $\Sigma$ of infinite type which has Thompson's group $\mathcal{T}$ as asymptotic mapping class group. We construct the asymptotic pants complex $\mathcal{C}$ of $\Sigma$ and prove that the group $\mathcal{T}$ acts transitively by automorphisms on it. Finally, we establish that the automorphism group of the complex $\mathcal{C}$ is an extension of the Thompson group $\mathcal{T}$ by $\mathbb{Z}/2\mathbb{Z}$

Elliptic obstacle problems with measure data: Potentials and low order regularity

Tue, 19 Jun 2012 13:43 EDT

Christoph Scheven

Source: Publ. Mat., Volume 56, Number 2, 327--374.

Abstract:
We consider obstacle problems with measure data related to elliptic equations of $p$-Laplace type, and investigate the connections between low order regularity properties of the solutions and non-linear potentials of the data. In particular, we give pointwise estimates for the solutions in terms of Wolff potentials and address the questions of boundedness and continuity of the solution.

Un Théorème de Point Fixe sur les Espaces $L^p$

Tue, 19 Jun 2012 13:43 EDT

Marc Bourdon

Source: Publ. Mat., Volume 56, Number 2, 375--392.

Abstract:
We establish a fixed point theorem for group actions on $L^p$-spaces, which generalizes a theorem of Żuk and of Ballmann-Świą}tkowski to the case $p \neq 2$.

Intermediaries in Bredon (Co)homology and Classifying Spaces

Tue, 19 Jun 2012 13:43 EDT

Fotini Dembegioti, Nansen Petrosyan, Olympia Talelli

Source: Publ. Mat., Volume 56, Number 2, 393--412.

Abstract:
For certain contractible $G$-CW-complexes and $\mathfrak F$ a family of subgroups of $G$, we construct a spectral sequence converging to the $\mathfrak F$-Bredon cohomology of $G$ with $\mathrm{E}_1$-terms given by the $\mathfrak F$-Bredon cohomology of the stabilizer subgroups. As applications, we obtain several corollaries concerning the cohomological and geometric dimensions of the classifying space $E_{\mathfrak {F}}G$. We also introduce, for any subgroup closed class of groups $\mathfrak F$, a hierarchically defined class of groups and show that if a group $G$ is in this class, then $G$ has finite $\mathfrak F\cap G$-Bredon (co)homological dimension if and only if $G$ has jump $\mathfrak F\cap G$-Bredon (co)homology.

A degree problem for two algebraic numbers and their sum

Tue, 19 Jun 2012 13:43 EDT

Paulius Drungilas, Artūras Dubickas, Chris Smyth

Source: Publ. Mat., Volume 56, Number 2, 413--448.

Abstract:
For all but one positive integer triplet $(a,b,c)$ with $a\leqslant b\leqslant c$ and $b\leqslant 6$, we decide whether there are algebraic numbers $\alpha$, $\beta$ and $\gamma$ of degrees $a$, $b$ and $c$, respectively, such that $\alpha+\beta+\gamma=0$. The undecided case $(6,6,8)$ will be included in another paper. These results imply, for example, that the sum of two algebraic numbers of degree $6$ can be of degree $15$ but cannot be of degree $10$. We also show that if a positive integer triplet $(a,b,c)$ satisfies a certain triangle-like inequality with respect to every prime number then there exist algebraic numbers $\alpha$, $\beta$, $\gamma$ of degrees $a$, $b$, $c$ such that $\alpha+\beta+\gamma=0$. We also solve a similar problem for all $(a,b,c)$ with $a\leqslant b\leqslant c$ and $b\leqslant 6$ by finding for which $a$, $b$, $c$ there exist number fields of degrees $a$ and $b$ such that their compositum has degree $c$. Further, we have some results on the multiplicative version of the first problem, asking for which triplets $(a,b,c)$ there are algebraic numbers $\alpha$, $\beta$ and $\gamma$ of degrees $a$, $b$ and $c$, respectively, such that $\alpha\beta\gamma=1$.

On the Power Pseudovariety $\mathbf{PCS}$

Tue, 19 Jun 2012 13:43 EDT

K. Auinger

Source: Publ. Mat., Volume 56, Number 2, 467--471.

Abstract:
The pseudovariety $\mathbf{PCS}$ which is generated by all power semigroups of finite completely simple semigroups is characterized in various ways. For example, the equalities \mathbf{PCS}=\mathbf{J}\malcab\mathbf{CS} =\mathbf{BG}\malcab\mathbf{RB} are established. This resolves a problem raised by Kaďourek and leads to several transparent algorithms for deciding membership in $\mathbf{PCS}$.

On non-commuting sets in finite soluble CC-groups

Tue, 19 Jun 2012 13:43 EDT

Adolfo Ballester-Bolinches, John Cossey

Source: Publ. Mat., Volume 56, Number 2, 467--471.

Abstract:
Lower bounds for the number of elements of the largest non-commuting set of a finite soluble group with a CC-subgroup are considered in this paper

Sumari de volum 56, Volume Index, Pub. Mat., vol. 56 (2012)

Tue, 19 Jun 2012 13:43 EDT

Source: Publ. Mat., Volume 56, Number 2, --.

Two-weight norm inequalities for potential type and maximal operators in a metric space

Tue, 18 Dec 2012 13:11 EST

Anna Kairema

Source: Publ. Mat., Volume 57, Number 1, 3--56.

Abstract:
We characterize two-weight norm inequalities for potential type integral operators in terms of Sawyer-type testing conditions. Our result is stated in a space of homogeneous type with no additional geometric assumptions, such as group structure or non-empty annulus property, which appeared in earlier works on the subject. One of the new ingredients in the proof is the use of a finite collection of adjacent dyadic systems recently constructed by the author and T. Hytönen. We further extend the previous Euclidean characterization of two-weight norm inequalities for fractional maximal functions into spaces of homogeneous type.

A new characterization of Triebel-Lizorkin spaces on \boldmath$\mathbb R^n$

Tue, 18 Dec 2012 13:11 EST

Dachun Yang, Wen Yuan, Yuan Zhou

Source: Publ. Mat., Volume 57, Number 1, 57--82.

Abstract:
In this paper, the authors characterize the Triebel-Lizorkin space $\dot F^\alpha_{p,q}(\mathbb{R}^n)$ via a new square function $$S_{\alpha,q}(f)(x)=\left\{\sum_{k\in\mathbb{Z}} 2^{k\alpha q}\left|\frac1{|B(x,2^{-k})|}\int_{B(x,2^{-k})}[f(x)-f(y)]\,dy \right|^q \right\}^{1/q}$$ where $f\in L^1_{\operatorname{loc}}({\mathbb R}^n)\cap \mathcal{S}'({\mathbb R}^n)$, $x\in{\mathbb R}^n$, $\alpha\in(0,2)$ and $p, q\in(1,\infty]$. Similar characterizations are also established for Triebel-Lizorkin spaces $\dot F^\alpha_{p,q}(\mathbb{R}^n)$ with $\alpha\in(0,\infty)\setminus 2{\mathbb N}$ and $p,q\in(1,\,\infty]$, and for Besov spaces $\dot B^\alpha_{p,q}(\mathbb{R}^n)$ with $\alpha\in(0,\infty)\setminus 2{\mathbb N}$, $p\in(1,\infty]$ and $q\in(0,\infty]$.

On the influence of transitively normal subgroups on the structure of some infinite groups

Tue, 18 Dec 2012 13:11 EST

Leonid A. Kurdachenko, Javier Otal

Source: Publ. Mat., Volume 57, Number 1, 83--106.

Abstract:
A transitively normal subgroup of a group $G$ is one that is normal in every subgroup in which it is subnormal. This concept is obviously related to the transitivity of normality because the latter holds in every subgroup of a group $G$ if and only if every subgroup of $G$ is transitively normal. In this paper we describe the structure of a group whose cyclic subgroups (or a part of them) are transitively normal.

On rings whose modules have nonzero homomorphisms to nonzero submodules

Tue, 18 Dec 2012 13:11 EST

Y. Tolooei, M. R. Vedadi

Source: Publ. Mat., Volume 57, Number 1, 107--122.

Abstract:
We carry out a study of rings $R$ for which $\operatorname{Hom}_R(M,N)\neq 0$ for all nonzero $ N\leq M_R$. Such rings are called retractable. For a retractable ring, Artinian condition and having Krull dimension are equivalent. Furthermore, a right Artinian ring in which prime ideals commute is precisely a right Noetherian retractable ring. Retractable rings are characterized in several ways. They form a class of rings that properly lies between the class of pseudo-Frobenius rings, and the class of max divisible rings for which the converse of Schur's lemma holds. For several types of rings, including commutative rings, retractability is equivalent to semi-Artinian condition. We show that a Köthe ring $R$ is an Artinian principal ideal ring if and only if it is a certain retractable ring, and determine when $R$ is retractable.

Degree of the first integral of a pencil in \boldmath$\mathbb{P}^2$ defined by Lins Neto

Tue, 18 Dec 2012 13:11 EST

Liliana Puchuri Medina

Source: Publ. Mat., Volume 57, Number 1, 123--137.

Abstract:
Let $\mathcal{P}_4$ be the linear family of foliations of degree $4$ in $\mathbb{P}^2$ introduced by A. Lins Neto, whose set of parameter with first integral $I_p(\mathcal{P}_4)$ is dense and countable. In this work, we will compute explicitly the degree of the rational first integral of the foliations in this linear family, as a function of the parameter.

On the fixed-point set of an automorphism of a group

Tue, 18 Dec 2012 13:11 EST

B. A. F. Wehrfritz

Source: Publ. Mat., Volume 57, Number 1, 139--153.

Abstract:
Let $\phi$ be an automorphism of a group $G$. Under various finiteness or solubility hypotheses, for example under polycyclicity, the commutator subgroup $[G, \phi]$ has finite index in $G$ if the fixed-point set $C_{G}(\phi)$ of $\phi$ in $G$ is finite, but not conversely, even for polycyclic groups $G$. Here we consider a stronger, yet natural, notion of what it means for $[G, \phi]$ to have 'finite index' in $G$ and show that in many situations, including $G$ polycyclic, it is equivalent to $C_{G}(\phi)$ being finite.

Flux limited generalized porous media diffusion equations

Tue, 18 Dec 2012 13:11 EST

V. Caselles

Source: Publ. Mat., Volume 57, Number 1, 144--217.

Abstract:
We study a class of generalized porous media type flux limited diffusion equations and we prove the existence and uniqueness of entropy solutions. We compute the Rankine-Hugoniot condition on the jump set for solutions which are of locally bounded variation in space and time. We give also a geometric characterization of the entropy conditions on the jump set for a restricted class of this type of equations.

Convexity of strata in diagonal pants graphs of surfaces

Tue, 18 Dec 2012 13:11 EST

J. Aramayona, C. Lecuire, H. Parlier, K. J. Shackleton

Source: Publ. Mat., Volume 57, Number 1, 219--237.

Abstract:
We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson completion. As a consequence, we exhibit convex flat subgraphs of every possible rank inside the diagonal pants graph.

Local maximal operators on measure metric spaces

Tue, 18 Dec 2012 13:11 EST

Chin-Cheng Lin, Krzysztof Stempak, Ya-Shu Wang

Source: Publ. Mat., Volume 57, Number 1, 239--264.

Abstract:
The notion of local maximal operators and objects associated to them is introduced and systematically studied in the general setting of measure metric spaces. The locality means here some restrictions on the radii of involved balls. The notion encompasses different definitions dispersed throughout the literature. One of the aims of the paper is to compare properties of the 'local' objects with the 'global' ones (i.e. these with no restrictions on the radii of balls). An emphasis is put on the case of locality function of Whitney type. Some aspects of this specific case were investigated earlier by two out of three authors of the present paper.