分数次积分交换子在加权Herz型Hardy空间上的有界性质

本文研究了由分数次积分I_l与加权Lipschitz函数b生成的交换子[b,I_l]在加权Herz型Hardy空间上的估计.利用加权Herz型Hardy空间的分解理论,得到了交换子[b,I_l]从加权Herz型Hardy空间到(弱)加权Herz空间上的有界性质.     

广义分数次积分算子在加权Herz型Hardy空间的有界性

利用加权Herz型Hardy空间的原子分解理论,讨论了广义分数次积分算子Tl从加权Lp空间到加权Lq空间,以及从加权Herz型Hardy空间到加权Herz空间的有界性问题.将已有的分数次积分算子的结论推广到广义分数次积分算子的情形.     

Calderon-Zygmund型算子在加权Herz型Hardy空间上的弱型估计

本文引入了加权弱Herz型Hardy空间，并证明了当a=n(1-1/q) δ时，胡国恩和陆善镇等在文[1]中所考虑的两类Calderon-Zygmund型算子分别连续地映加权Herz型Hardy空间到加权弱Herz空间和加权弱Herz型Hardy空间。     

奇异积分交换子在加权Herz型Hardy空间上的有界性质

T_b表示由加权Lipschitz函数b与Calderon-Zygmund奇异积分算子T生成的交换子.研究了T_b在加权Herz型Hardy空间上的有界性质,并在端点处证明了交换子是从加权Herz型Hardy空间到加权弱Herz空间的有界算子.     

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.     

加权Herz型Hardy空间的分子刻画

首先定义了加权Herz型Hardy空间上的分子并证明了其分子刻画。作为应用,给出了强奇异积分算子T_b在加权Herz和Hardy空间上有界性的证明。     

Weighted estimates for commutators of higher dimensional Hardy operators

得到了由加权Lipschitz函数(或加权CMO函数)和n维Hardy算子生成的交换子在一些函数空间的有界性,例如加权Lebesgue空间,加权Herz型空间.     

分数次Hardy算子的广义交换子在Herz型Hardy空间上的端点估计（英文）

本文证明了分数次Hardy算子广义交换子是Herz型Hardy空间到Herz空间有界的,当且仅当交换子为零算子.因此,本文用了一个弱型估计代替,即交换子由Herz型Hardy空间到弱Herz空间有界.     

广义Calderón-Zygmund算子交换子在Hardy型空间上的有界性

[b,T]表示由Lipschitz函数b与广义Calderon-Zygmund算子T生成的交换子．本文研究了[b,T]在经典Hardy空间和Herz型Hardy空间上的有界性,并且在临界点情形证明了该交换子是从Hardy空间到弱Lebesgue空间以及Herz型Hardy到弱Herz空间有界的．     

向量值广义Calderón-Zygmund算子在Herz型Hardy空间上的有界性

文中完善了参考文献[5]中的结论,在通常的标准假设下,证明了一类具有向量值核的广义Calderón-Zygmund算子从Herz型Hardy空间HKp到向量值Herz空间KE,p的有界性及加权有界性.     

Anisotropic Herz-type Hardy spaces with variable exponent and their applications

A class of anisotropic Herz-type Hardy spaces with variable exponent associated with a non-isotropic dilation on \({\mathbb{R}^{n}}\) are introduced, and characterizations of these spaces are established in terms of atomic and molecular decompositions. As some applications of the decomposition theory, the authors study the interpolation problem and the boundedness of a linear operator on the anisotropic Herz-type Hardy spaces with variable exponent.     

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.     

Boundedness of Commutators on Hardy-Type Spaces

In this paper, the boundedness of the commutator generated by strongly singular Calderón-Zygmund operator and a Lipschitz function is discussed on the classical Hardy spaces and the Herz-type Hardy spaces. The authors also get the boundedness of the strongly singular Calderón-Zygmund operator itself and the commutator generated by strongly singular Calderón-Zygmund operator and a BMO function on the Herz-type Hardy spaces.     

Two-Weighted Inequalities for Hausdorff Operators in Herz-Type Hardy Spaces

Mathematical Notes - In this paper, we prove the boundedness of matrix Hausdorff operators and rough Hausdorff operators in the two weighted Herz-type Hardy spaces associated with both power...     

Boundedness of generalized fractional integrals in weighted Herz-type spaces

In this paper, the authors investigate the boundedness of the generalized fractional integrals of Pérez on the weighted Herz spaces, the weighted weak Herz spaces and the weighted Herz-type Hardy spaces for general weights.     

Potential Operators in Weighted Herz-Type Spaces over Locally Compact Vilenkin Groups

Let G be a bounded locally compact Vilenkin group. We study the boundedness of potential operators and the maximal operators associated with them in the weighted Herz space, the weighted Hardy space and the weighted Herz-type Hardy space over G. We also discuss the boundedness of these operators on the weighted weak Lebesgue space and the weighted weak Herz space whose sharpness are also discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

New hardy spaces associated with some anisotropic Herz spaces and their applications

In this paper, a class of anisotropic Herz-type Hardy spaces associated with a non-isotropic dilation on ℝ ⁿ are introduced, and the central atomic and molecular decomposition characterizations of those spaces are established. As some applications of the decomposition theory, the authors study the interpolation problem and the boundedness of the central δ-Calderón-Zygmund operators on the anisotropic Herz-type Hardy spaces. The research is supported by NSF of China (Grant Nos. 10571014 and 10571015) and SRFDP of China (Grant No. 20050027025)     

Weighted Estimates for Commutators of Strongly Singular Calderón–Zygmund Operators

In this paper,the authors establish the boundedness of commutators generated by strongly singular Calderón–Zygmund operators and weighted BMO functions on weighted Herz-type Hardy spaces.Moreover,the corresponding results for commutators generated by strongly singular Calderón–Zygmund operators and weighted Lipschitz functions can also be obtained.