Interpolation for weak Orlicz spaces with M Δ condition

An interpolation theorem for weak Orlicz spaces generalized by N-functions satisfying M _Δ condition is given. It is proved to be true for weak Orlicz martingale spaces by weak atomic decomposition of weak Hardy martingale spaces. And applying the interpolation theorem, we obtain some embedding relationships among weak Orlicz martingale spaces. This work was supported by the National Natural Science Foundation of China (Grant No. 10671147)     

Interpolation for weak Orlicz spaces with M Δ condition

An interpolation theorem for weak Orlicz spaces generalized by N-functions satisfying M _Δ condition is given. It is proved to be true for weak Orlicz martingale spaces by weak atomic decomposition of weak Hardy martingale spaces. And applying the interpolation theorem, we obtain some embedding relationships among weak Orlicz martingale spaces.     

Maximal functions,Hardy spaces and Fourier multiplier theorems on unbounded Vilenkin groups

We consider relations between various existing concepts of Hardy spaces on Vilenkin groups. The problem of an appropriate Fourier multiplier theorem for unbounded Vilenkin groups is revisited and the conditions made more precise under which such a theorem is established. Theorem 3.1 from Avdispahi? and Memi? (2010) [1] is rectified.     

Sharp Embedding Relations Between Local Hardy and α-Modulation Spaces

Analysis Mathematica - In this paper, we give optimal embedding relations between local Hardy spaces and α-modulation spaces. By a different approach, we extend the main results obtained by...     

A special case of de Branges' theorem on the inverse monodromy problem

We give a new proof of a special case of de Branges' theorem on the inverse monodromy problem: when an associated Riemann surface is of Widom type with Direct Cauchy Theorem. The proof is based on our previous result (with M.Sodin) on infinite dimensional Jacobi inversion and on Levin's uniqueness theorem for conformal maps onto comb-like domains. Although in this way we can not prove de Branges' Theorem in full generality, our proof is rather constructive and may lead to a multi-dimensional generalization. It could also shed light on the structure of invariant subspaces of Hardy spaces on Riemann surfaces of infinite genus.This work was supported by the Austrian Founds zur Förderung der wissenschaftlichen Forschung, project-number P12985-TEC     

Anisotropic weak Hardy spaces and interpolation theorems

In this paper, the authors establish the anisotropic weak Hardy spaces associated with very general discrete groups of dilations. Moreover, the atomic decomposition theorem of the anisotropic weak Hardy spaces is also given. As some applications of the above results, the authors prove some interpolation theorems and obtain the boundedness of the singular integral operators on these Hardy spaces.     

Sharpness of some properties of weighted modulation spaces

We obtain some optimal properties on weighted modulation spaces. We find the necessary and sufficient conditions for product inequalities, convolution inequalities and embedding on weighted modulation spaces. Especially, we establish the analogue of the sharp Sobolev embedding theorem on weighted modulation spaces.     

Fourier multipliers on the real Hardy spaces

We provide a variant of Hytönen’s embedding theorem, which allows us to extend and unify several sufficient conditions for a function to be a Fourier multiplier on the real Hardy spaces.     

A convexity theorem for noncommutative gradient flows

In this survey we shall prove a convexity theorem for gradient actions of reductive Lie groups on Riemannian symmetric spaces. After studying general properties of gradient maps, this proof is established by (1) an explicit calculation on the hyperbolic plane followed by a transfer of the results to general reductive Lie groups, (2) a reduction to a problem on abelian spaces using Kostant's Convexity Theorem, (3) an application of Fenchel's Convexity Theorem. In the final section the theorem is applied to gradient actions on other homogeneous spaces and we show, that Hilgert's Convexity Theorem for moment maps can be derived from the results.     

Multiplier theorems for Herz type Hardy spaces

In this paper, the authors establish a multiplier theorem for Herz type Hardy spaces.

     

Landau–Bloch Constants for Functions in α-Bloch Spaces and Hardy Spaces

In this paper, we obtain a sharp distortion theorem for a class of functions in ??-Bloch spaces, and as an application of it, we establish the corresponding Landau??s theorem. These results generalize the corresponding results of Bonk, Minda and Yanagihara, and Liu, respectively. We also prove the existence of Landau?CBloch constant for a class of functions in Hardy spaces and the obtained result is a generalization of the corresponding result of Chen and Gauthier.     

B值弱Hardy两指标鞅空间的原子分解

本文研究了B值弱Hardy两指标鞅空间的原子分解理论,利用原子分解的方法, 获得了B值弱Hardy两指标鞅空间的相互嵌入关系,所得结果联系于Banach空间的几何性质.     

On the Sobolev embedding theorem for variable exponent spaces in the critical range

In this paper we study the Sobolev embedding theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. The proof is based on a suitable refinement of the estimates in the Concentration–Compactness Theorem for variable exponents and an adaptation of a convexity argument due to P.L. Lions, F. Pacella and M. Tricarico.     

Multiplicity of solutions for differential inclusion problems in {\mathbb{R}^N} involving the p(x)-Laplacian

In this paper we consider the differential inclusion problem in ${\mathbb{R}^N}$ involving the p(x)-Laplacian of the type $$ -\triangle_{p(x)} u+V(x)|u|^{p(x)-2}u\in \partial F(x,u)\,\,\,{\rm in}\, \mathbb{R}^N. $$ The approach used in this paper is the variational method for locally Lipschitz functions. More precisely, based on the Weirstrass Theorem and Mountain Pass Theorem, we get there exist at least two nontrivial solutions. We also establish a Bartsch–Wang type compact embedding theorem for variable exponent spaces.     

On a tauberian theorem of Hardy and Littlewood

In this paper, we give a simple alternative proof of a Tauberian theorem of Hardy and Littlewood (Theorem E stated below, [3]).     

Calderón-Zygmund operaors on the Hardy spaces of weighted Herz type

Applying the decomposition theorems in [1] and [2], we obtain the boundedness theorem of Calderón-Zygmund operator of type δ on the Hardy spaces of weighted Herz type and establish interpolation theorem of linear operators on the weighted Herz spaces. Supported by NSF of China and the Fund of Doctoral Program of N.E.C.     

调和函数的Lipschitz型空间和Landau-Bloch型定理

主要研究调和函数和Poisson方程的解的性质.讨论了调和函数的Lipschitz型空间,建立了调和函数的Schwarz-Pick型引理,并利用所得结果证明了与调和Hardy空间有关的一个Landau-Bloch型定理.最后,还利用正规族理论讨论了与Poisson方程的解有关的Landau-Bloch型定理的存在性.     

Sobolev‐Jawerth embedding of Triebel‐Lizorkin‐Morrey‐Lorentz spaces and fractional integral operator on Hardy type spaces

A Sobolev type embedding for Triebel‐Lizorkin‐Morrey‐Lorentz spaces is established in this paper. As an application of this result, the boundedness of the fractional integral operator on some generalizations of Hardy spaces such as Hardy‐Morrey spaces and Hardy‐Lorentz spaces are obtained.     

Bilinear pseudo-differential operators on local hardy spaces

In this paper, the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type (1, 0) in the sense of Ho¨rmander and use the atomic decompositions of local Hardy spaces to establish the boundedness of the bilinear pseudo-differential operators and the bilinear singular integral operators on the product of local Hardy spaces.     

Real interpolation between martingale hardy and BMO spaces

In this paper, we consider the real interpolation with a function parameter between martingale Hardy and BMO spaces. An interpolation theorem for martingale Hardy and BMO spaces is formulated. As an application, real interpolation between martingale Lorentz and BMO spaces is given.