多复变中正规权Zygmund空间上的几个性质

黎深莲, 张学军

数学学报 ›› 2019, Vol. 62 ›› Issue (5) : 795-808.

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数学学报 ›› 2019, Vol. 62 ›› Issue (5) : 795-808. DOI: 10.12386/A2019sxxb0073
论文

多复变中正规权Zygmund空间上的几个性质

    黎深莲, 张学军
作者信息 +

Several Properties on the Normal Weight Zygmund Space in Several Complex Variables

    Shen Lian LI, Xue Jun ZHANG
Author information +
文章历史 +

摘要

本文讨论了多复变中单位球上正规权Zygmund空间ZμB)的一些性质.首先给出了ZμB)函数的一种积分表示,接着证明了ZμB)是正规权Bergman空间Aν1B)的对偶空间,其对偶对按如下形式给出:

其中νρ)=(1-ρ2β+1μ-1ρ)(0 ≤ ρ<1)并且β>max{0,b-1}.最后作为积分表示和对偶的一个应用,作者给出了ZμB)中每个函数的一个原子分解.

Abstract

In this paper, the authors investigate some properties of the normal weight Zygmund space Zμ(B) in several complex variables. Firstly, the authors establish an integral representation of function in Zμ(B). Secondly, the authors show that Zμ(B) can be identified with the dual space of the normal weight Bergman space Aν1 (B) under the integral pairing

where ν(r)=(1-r2)β+1μ-1(r) (0 ≤ r<1) and β>max{0, b-1}. Finally, as an application of the integral representation and the dual, the authors give an atomic decomposition for every function in Zμ(B).

关键词

正规权Zygmund空间 / 积分表示 / 对偶 / 原子分解 / 单位球

Key words

normal weight Zygmund space / integral representation / duality / atomic decomposition / unit ball

引用本文

导出引用
黎深莲, 张学军. 多复变中正规权Zygmund空间上的几个性质. 数学学报, 2019, 62(5): 795-808 https://doi.org/10.12386/A2019sxxb0073
Shen Lian LI, Xue Jun ZHANG. Several Properties on the Normal Weight Zygmund Space in Several Complex Variables. Acta Mathematica Sinica, Chinese Series, 2019, 62(5): 795-808 https://doi.org/10.12386/A2019sxxb0073

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基金

国家自然科学基金资助项目(11571104);湖南省研究生科研创新资助项目(CX2017B220)

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