In this paper, the endpoint estimates for some multilinear operators related to certain fractional singular integral operators on Herz and Herz type Hardy spaces are obtained.

In this paper we establish two inverse theorems for Bernstein-Chlodowsky type polynomials of two variables in a rectangular and a triangular domain.

The main result of this paper are a criteria giving conditions that the certain infinite sequence of rational numbers be linearly unrelated. The proof is direct and does not require any special theorems.

In this study, we show that a generalized helicoid with null axis is isometric to a rotation surface with null axis so that helices on the helicoid correspond to parallel circles on the rotation surface in three dimensional Minkowski space. Moreover, we obtained that these surfaces are minimal. An addition, if these surfaces have the same Gauss map, we can determine them.

Total stability for systems of ordinary differential equations, functional differential equations, and difference equations was introuced. In this paper, we will extend this notion to the so-called total $\phi _{0}$-stability for systems of difference equations. given some new criteria and results. Our technique depends on cone-valued Liapunov’s function method.

Characters of factor representations of finite type of the wreath products $G = \mathfrak{S}_{\infty}(T)$ of any compact groups $T$ with the infinite symmetric group $\mathfrak{S}_{\infty}$ were explicitly given in [HH4]-[HH6], as the extremal continuous positive definite class functions $f_{A}$ on $G$ determined by a parameter $A$. In this paper, we give a special kind of realization of a factor representation $\pi ^{A}$ associated to $f_{A}$. This realization is better than the Gelfand-Raikov realization $\pi _{f}$, $f = f_{A}$, in [GR] at least at the point where a matrix element $\langle \pi ^{A}(g)v_{0}, v_{0}\rangle$ of $\pi ^{A}$ for a cyclic vector $v_{0}$ can be calculated explicitly, which is exactly equal to the character $f_{A}$ (and so $\pi ^{A}$ has a trace-element $v_{0}$). So the positive-definiteness of class functions $f_{A}$ given in [HH4]-[HH6] is automatically guaranteed, a proof of which occupies the first half of [HH6] in the case of $T$ infinite. The case where $T$ is abelian contains the cases of infinite Weyl groups and the limits $\mathfrak{S}_{\infty}(\mathbf{Z}_{r}) = \lim _{n\to\infty}G(r,1,n)$ of complex reflexion groups.

We will propose a sufficient condition which guarantees the pathwise uniqueness for jump type equations in multi-dimensional case. An example given in Section 3 shows that the condition is nearly best possible. Comparing our results with those known in the case of Brownian equations, we claim that essential difference between these two cases. It seems to be remarkable that we could explain these phenomena in the language of the Potential theory. Our principal method in the paper is based on the Fourier analysis, where effective tools such as Bessel functions, hypergeometric functions play essential roles.

We prove that the Laplace-Beltrami operator commutes with the Berezin transform on a Kähler manifold if and only if it is a Hermitian symmetric space.

We will construct an isomorphism of the group of all cobordism classes of fold-maps of degree 0 of $n$-dimensional closed oriented manifolds to the $n$-sphere to the $n$-th stable homotopy group $\pi _{n}^{s}$ of spheres. As an application we will show that elements of $\pi _{n}^{s}$ are detected by higher singularities of certain maps in dimensions $n < 8$.

In this paper we discuss the two-point boundary value problem of third order ordinary differential inclusions in ordered Banach Spaces. By using a fixed point theorem due to Hong [8], we establish the existence of solutions the mentioned above problems with discontinuous right hand side.

A four-dimensional non-integrable almost Hermitian manifold whose second twistor space is a complex manifold is given.

Let $E = \{\ldots ,-2,-1, 0, 1, 2, \ldots \}$. Given a uni-instantaneous bilateral birth-death pre-generator matrix $Q = (q_{ij})$ defined on $E \times E$, we investigate the existence conditions for the corresponding birth-death $Q$-processes, and furthermore, construct all the processes when the existence conditions are satisfied. In addition, the uniqueness of the honest $Q$-processes are investigated as well.