Let $X$ be a metric space with doubling measure and $L$ be an operator which satisfies Davies–Gaffney heat kernel estimates and has a bounded $H_\infty$ functional calculus on $L^2(X)$. In this paper, we develop a theory of Musielak–Orlicz Hardy spaces associated to $L$, including a molecular decomposition, square function characterization and duality of Musielak–Orlicz Hardy spaces $H_{L,\omega}(X)$. Finally, we show that $L$ has a bounded holomorphic functional calculus on $H_{L,\omega}(X)$ and the Riesz transform is bounded from $H_{L,\omega}(X)$ to $L^1(\omega)$.

We study the rate of convergence for the renewal density with the interarrival times that are absolutely continuous, not necessarily positive, and has finite moment of $\alpha$th order with $\alpha$ > 3/2. We obtain an error estimate that is better than known results. Our method is based on modification of functions that have the same tails as the original ones and have integrable Fourier transform.

We give a complete description of all self-injective artin algebras of infinite representation type whose component quiver has no short cycles.

We consider in this paper the family of exponential Lie groups $G_{n,\mu}$, whose Lie algebra is an extension of the Heisenberg Lie algebra by the reals and whose quotient group by the centre of the Heisenberg group is an $ax+b$-like group. The C*-algebras of the groups $G_{n,\mu}$ give new examples of almost $C_0({\cal K})$-C*-algebras.

The purpose of the paper is to study coefficient multipliers of the Hardy spaces $H^p([0,\infty))$ (0 < $p$ < 1) associated with Laguerre expansions. As a consequence, a Paley type inequality is obtained.

We give a classification of all complex Delsarte surfaces with only isolated ADE singularities. This results in 83 types of surfaces. For each of these types, we give a closed formula for the Picard number depending only on the degree.

The notion of the weighted degree of a polynomial is a basic tool in Affine Algebraic Geometry. In this paper, we study the properties of the weighted multidegrees of polynomial automorphisms by a new approach which focuses on stable coordinates. We also present some applications of the generalized Shestakov-Umirbaev theory.

In [6], Kotschick and Morita showed that the Gel'fand–Kalinin–Fuks class in ${\mathrm{H}^{7}_{\rm GF} ( {\mathfrak{ham}}_{2}, {\mathfrak{sp}}(2,\mathbb{R}))_{8}}$ is decomposed as a product $\eta \wedge \omega$ of some leaf cohomology class $\eta$ and a transverse symplectic class $\omega$. We show that the same formula holds for the Metoki class, which is a non-trivial element in ${\mathrm{H}^{9}_{\rm GF} ( {\mathfrak{ham}}_{2}, {\mathfrak{sp}}(2,\mathbb{R}))_{14}}$. The result was conjectured in [6], where they studied characteristic classes of transversely symplectic foliations due to Kontsevich. Our proof depends on Gröbner Basis theory using computer calculations.

We study the boundedness of integral operators of convolution type in the Lebesgue spaces with weights. As a byproduct, we give a simple proof of the fact that the standard Sobolev space $H^s(\mathbb{R}^n)$ forms an algebra for $s$ > $n/2$. Moreover, an optimality criterion is presented in the framework of weighted $L^p$-boundedness.

We study the existence of weak solution for unsteady fluid-structure interaction problem for shear-thickening flow. The time dependent domain has at one part a flexible elastic wall. The evolution of fluid domain is governed by the generalized string equation with action of the fluid forces. The power-law viscosity model is applied to describe shear-dependent non-Newtonian fluids.

Weil's representation is a basic object in representation theory which plays a crucial role in many places: construction of unitary irreducible representations in the frame of the orbit method, Howe correspondence, Theta series, … The decomposition in irreducibles of the restriction of Weil's representation to maximal compact subgroups or anisotropic tori of the metaplectic group is thus an important information in representation theory. Except for $SL(2)$, this was not known in the p-adic case. In this article, we prove that the restriction of the Weil representation over a p-adic field, $p\neq2$, to maximal compact subgroups is multiplicity free and give an explicit description of the irreducibles occurring. In another paper, using our results, we describe the decomposition of the restriction of the Weil representation to maximal elliptic tori.

We consider the initial value problem for the Oseen system in plane exterior domains and study the large time behavior of solutions. For the space dimension $n\geq 3$ the theory was well developed by [26], [10] and [11], while 2D case has remained open because of difficulty arising from singularity like $\log\sqrt{\lambda+\alpha^2}$ of the Oseen resolvent, where $\lambda$ is the resolvent parameter and $\alpha$ is the Oseen parameter. In this paper we derive the local energy decay of the Oseen semigroup and apply it to deduction of $L^q$-$L^r$ estimates. The dependence of estimates on the Oseen parameter $\alpha$ is also discussed. The proof relies on detailed analysis of asymptotic structure of the fundamental solution of the Oseen resolvent with respect to both $\lambda$ and $\alpha$.

The aim of this paper is to give a unifying description of various constructions of sites (subanalytic, semialgebraic, o-minimal) and consider the corresponding theory of sheaves. The method used applies to a more general context and gives new results in semialgebraic and o-minimal sheaf theory.

We compute the norm of some bilinear forms on products of weighted Besov spaces in terms of the norm of their symbol in a space of pointwise multipliers related to a space of Carleson measures.

Let $R$ be a Noetherian prime ring with an automorphism $\sigma$ and a left $\sigma$-derivation $\delta$, and let $X$ be an invertible ideal of $R$ with $\sigma(X) = X$. We define an Ore-Rees ring $S = R[Xt; \sigma, \delta]$ which is a subring of an Ore extension $R[t; \sigma, \delta]$, where $t$ is an indeterminate. It is shown that if $R$ is a maximal order, then so is $S$. In case $\sigma = 1$, we define the concepts of $(\delta; X)$-stable ideals of $R$ and of $(\delta; X)$-maximal orders and prove that $S$ is a maximal order if and only if $R$ is a $(\delta; X)$-maximal order. Furthermore we give a complete description of v-$S$-ideals, which is used to characterize $S$ to be a generalized Asano ring. In case $\delta = 0$, we define the concepts of $(\sigma; X)$-invariant ideals of $R$ and of $(\sigma; X)$-maximal orders in order to show that $S$ is a maximal order if and only if $R$ is a $(\sigma; X)$-maximal order. We also give examples $R$ such that either $R$ is a $(\delta; X)$-maximal order or is a $(\sigma; X)$-maximal order but they are not maximal orders.

We introduce a generalized coderivation from a bicomodule to a bicomodule over corings, which is a generalization of a coderivation. For each $({\mathcal D},{\mathcal C})$-bicomodule $N$ over corings ${\mathcal C}$ and ${\mathcal D}$, we construct the universal generalized coderivation $\upsilon_N:{\mathcal U}(N)\to N$ such that every generalized coderivation from a $({\mathcal D},{\mathcal C})$-bicomodule $M$ to $N$ is uniquely expressed as $\upsilon_N\circ f$ with some $({\mathcal D},{\mathcal C})$-bicomodule map $f:M\to{\mathcal U}(N)$. ${\mathcal U}(N)$ is isomorphic to the cotensor product of $N$ and ${\mathcal U}({\mathcal D}\otimes_R{\mathcal C})$. We show that a coring ${\mathcal C}$ is coseparable if and only if, for any coring ${\mathcal D}$, all generalized coderivations from a $({\mathcal D},{\mathcal C})$-bicomodule to a $({\mathcal D},{\mathcal C})$-bicomodule are inner.

In this paper, we consider conformal invariants defined by various spaces of harmonic functions on Riemann surfaces. The Harnack distance is a typical one. We give sharp inequalities comparing those invariants with the hyperbolic metric on the Riemann surface and we determine when equalities hold. We also describe the Harnack distance in terms of the Martin compactification and discuss some properties of the distance.