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多复变中正规权Zygmund空间上的几个性质

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多复变中正规权Zygmund空间上的几个性质 黎深莲, 张学军湖南师范大学数学与统计学院 长沙 410006 Several Properties on the Normal Weight Zygmund Space in Several Complex Variables Shen Lian LI, Xue Jun ZHANGCollege of Mathematics and Statistics, Hunan Normal University, Changsha 410006, P. R. China
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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.
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收稿日期: 2018-05-29
MR (2010):O174.56
基金资助: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)
通讯作者:张学军E-mail: xuejunttt@263.net
作者简介: 黎深莲,E-mail:201710100077@smail.hunnu.edu.cn
引用本文:
黎深莲, 张学军. 多复变中正规权Zygmund空间上的几个性质[J]. 数学学报, 2019, 62(5): 795-808. 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.
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http://www.actamath.com/Jwk_sxxb_cn/CN/ http://www.actamath.com/Jwk_sxxb_cn/CN/Y2019/V62/I5/795


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