Weighted Composition Operators on Spaces of Analytic Functions on the Complex Half-Plane
Weighted Composition Operators on Spaces of Analytic Functions on the Complex Half-Plane
复制标题
复半平面解析函数空间上的加权复合算子
DOI：
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发表时间：
2016
影响因子：
0.8
通讯作者：
Andrzej S. Kucik
中科院分区：
文献类型：
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作者：
Andrzej S. Kucik
在本文中，我们将展示如何用卡尔森测度和伯格曼核来描述称为 Zen 空间（包括 Hardy 空间和加权 Bergman 空间）的开右复半平面上的一类解析函数空间上的加权合成算子的有界条件。在希尔伯特设置中，我们还将展示这些空间上的因果加权复合算子的范数如何相互关联，并用它来显示（未加权）复合算子Cφdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$C_varphi $$end{document} 限定在 Zen 空间上当且仅当 φdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$varphi $$end{document} 在无穷远处有有限的角度导数。最后，我们将证明 Zen 空间上不存在紧致组合算子。
In this paper we will show how the boundedness condition for the weighted composition operators on a class of spaces of analytic functions on the open right complex half-plane called Zen spaces (which include the Hardy spaces and weighted Bergman spaces) can be stated in terms of Carleson measures and Bergman kernels. In Hilbertian setting we will also show how the norms of causal weighted composition operators on these spaces are related to each other and use it to show that an (unweighted) composition operatorCφdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$C_varphi $$end{document} is bounded on a Zen space if and only if φdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$varphi $$end{document} has a finite angular derivative at infinity. Finally, we will show that there is no compact composition operator on Zen spaces.