多复变中正规权Zygmund空间上的几个性质
Several Properties on the Normal Weight Zygmund Space in Several Complex Variables
本文讨论了多复变中单位球上正规权Zygmund空间Zμ(B)的一些性质.首先给出了Zμ(B)函数的一种积分表示,接着证明了Zμ(B)是正规权Bergman空间Aν1(B)的对偶空间,其对偶对按如下形式给出:
其中ν(ρ)=(1-ρ2)β+1μ-1(ρ)(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Zμ(B)中每个函数的一个原子分解.
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).
正规权Zygmund空间 / 积分表示 / 对偶 / 原子分解 / 单位球 {{custom_keyword}} /
normal weight Zygmund space / integral representation / duality / atomic decomposition / unit ball {{custom_keyword}} /
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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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