Algebraic Properties of Dual Toeplitz Operators on Harmonic Hardy Space over Polydisc

In this paper,we introduce the harmonic Hardy space on T~n and study some algebraic properties of dual Toeplitz operator on the harmonic Hardy space on T~n.     

多圆盘调和Hardy空间上对偶Toeplitz的代数性质

本文给出多圆盘上的调和Hardy空间的定义, 并且给出多圆盘调和Hardy空间上对偶对偶Toeplitz算子的某些代数性质.     

Operator theory in the Hardy space over the bidisk (I)

In this paper, we identify the vector valued Hardy space with the Hardy space over the bidisk and construct a universal model for thecontractive analytic functions. We will also study some elementary properties of the submodules and show, in some cases, how the operator theoretical properties are related to the module theoretical properties. The last part focus on the study of double commutativity of compression operators.     

On slice hyperholomorphic fractional Hardy spaces

In this paper we introduce and study the fractional Hardy spaces of the half space and of the unit ball in the quaternionic setting. In particular, we discuss their properties of invariance and of factorization in terms of functions in the Hardy space of the half space in the first case, and in terms of a suitable reproducing kernel Hilbert space in the case of the unit ball.     

Additive invariants on the Hardy space over the polydisc

In recent years various advances have been made with respect to the Nevanlinna-Pick kernels, especially on the symmetric Fock space, while the development on the Hardy space over the polydisc is relatively slow. In this paper, several results known on the symmetric Fock space are proved for the Hardy space over the polydisc. The known proofs on the symmetric Fock space make essential use of the Nevanlinna-Pick properties.Specifically, we study several integer-valued numerical invariants which are defined on an arbitrary invariant subspace of the vector-valued Hardy spaces over the polydisc. These invariants include the Samuel multiplicity, curvature, fiber dimension, and a few others.A tool used to overcome the difficulty associated with non-Nevanlinna-Pick kernels is Tauberian theory.     

Toeplitz算子Fredholm性质的局部化描述

利用Banach代数中的局部化定理描述Bergman空间上Toeplitz算子的Fredholm性质,证明了类似于Hardy空间上的一个局部化定理．讨论了L∞（D）的极大理想空间的一些性质．     

解析算子函数空间上的复合算子理论初步

本文将经典Hardy空间上复合算子的理论、方法应用到解析算子函数空间上,给出了解析算子函数空间的几个基本性质及复合算子的有界性条件.     

带有齐性核的分数次积分算子在Hardy型空间上的有界性

该文研究了带有齐性核的分数次积分算子T_(Ω,α)在一些Hardy空间上的映射性质,其中核Ω在球面S~(n-1)上满足一些L~S-Dini条件.作者将前人的一些结果改进到0αn情形,同时还得到了算子T_(Ω,α)在Herz型Hardy空间上的一个端点估计.     

A type theorem on the weighted Herz‐type Hardy spaces and applications

This paper gives a type theorem, which is a boundedness criterion for singular integral operators from the weighted Herz‐type Hardy spaces into the weighted local Herz‐type Hardy spaces. As applications, the corresponding mapping properties for the Cauchy integral and Calderón's commutators are obtained. In addition, a counter example is shown that neither is a Calderón–Zygmund singular integral operator bounded on the homogeneous local Herz‐type Hardy space, nor bounded on the classical local Hardy space.     

Marcinkiewicz积分交换子在一些Hardy空间的有界性

讨论了由核函数满足具有某类Dini条件的Marcinkiewicz积分μΩ及函数b∈Lipβ(R~n)生成的交换子μ(_Ω,b)~m的性质.证明了Marcinkiewicz积分交换子μ_(_Ω,b)~m在Hardy型空间H_(bm,s)(R~n)上有界,也在Herz型Hardy空间H_(bm)K_p~(a_q)(R~n)上有界.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

Integral operators on BMO and Campanato spaces

This paper establishes the mapping properties of integral operators on space of bounded mean oscillation and Campanato spaces. In particular, we have the Hardy’s inequality and the boundedness of the Hadamard fractional integrals on space of bounded mean oscillation and Campanato spaces.     

重调和Hardy空间上的Toeplitz 算子

与调和Bergman 空间相对应, 本文研究重调和Hardy 空间h²(D²) 上的Toeplitz 算子. 本文发现, h²(D²) 上的Toeplitz 算子与经典的Hardy 空间、Bergman 空间及调和Bergman 空间上的Toeplitz算子的性质都有很大的差异. 例如解析Toeplitz 算子可以不是半可换及可交换的. 即使半可换, 其中任何一个符号可以不为常数; 即使可交换, 两个符号的非平凡线性组合也不一定是常数. 本文得到了h²(D²) 上两个解析Toeplitz 算子半可换和可换的充分必要条件.     

Hardy空间上复合算子的伴随表示

Hardy空间上的复合算子的伴随算子具有很好的性质,但对一般情形而言,一直没有关于它的明确表达式．Cowen于1988年给出了(?)为D上的线性分式自映射情形时C*(?)的表达式,并且于2000年给出了n个变量情形的推广．他指出,正是由于没有一般情形的C*(?)的表达式,在很大程度上,阻碍了复合算子理论的发展．该文给出了Hardy空间上的复合算子伴随的准确表达式．     

Herz型空间中的Littlewood-Paley g函数

本文研究了包含 Ｌｉｔｔｌｅｗｏｏｄ－Ｐａｌｅｙ ｇ函数在内的一大类次线性算子从 Ｈｅｒｚ 空间到弱Ｈｅｒｚ空间ＷＫ中的有界 性;而当时,我们得到了ｇ函数从 Ｈｅｒｚ型 Ｈａｒｄｙ空间 ＨＫ（Ｒｎ）到 Ｈｅｒｚ空间或弱Ｈｅｒｚ空间ＷＫ（Ｒｎ）中的有界性．     

Divergence-free Hardy space on RN+

We introduce a divergence-free Hardy space Hz1,div(RN+,RN) and prove its divergence-free atomic decomposition. We also characterize its dual space and establish a "div-curl" type theorem on R+3 with an application to coercivity properties of some polyconvex quadratic forms.     

带有加权Lipschitz函数的交换子的有界性

研究了由加权Lipschitz函数b和Calderón-Zygmund奇异积分算子T生成的交换子Tb在一些加权空间上的有界性,涉及到加权Hardy空间,加权Herz空间及和加权Herz型Hardy空间.同时也得到了其相应的端点估计.     

Calderón-Zygmund算子在H_b~p空间上的有界性

众所周知,如果Calderón-Zygmund算子T满足T~*(1)=0,则算子T在H~p,n/(n+ε)相似文献   

一类调和映射的边界正则性

讨论一类映入球面的满足拟单调不等式的弱调和映射的边界正则性。利用函数的延拓技巧以及Hardy空间和BMO空间的对偶性，对这类弱调和映射的边界正则性给出一个简明的证明。     

A New Estimate for Bochner-Riesz Operators at the Critical Index on Weighted Hardy Spaces

Let w be a Muckenhoupt weight and Hwp （JRn） be the weighted Hardy space. In this paper, by using the atomic decomposition of Hwp（Rn）, we will show that the Bochner-Riesz operators TRδ are bounded from Hwp（Rn） to the weighted weak Hardy spaces WHwp （Rn） for 0 〈 p 〈 1 and δ = n/p- （n ＋ 1）/2. This result is new even in the unweighted case.