Holomorphic function spaces on homogeneous Siegel domains

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-09-23 DOI:10.4064/dm833-3-2021

Mattia Calzi, M. Peloso

引用次数: 16

Abstract

We study several connected problems of holomorphic function spaces on homogeneous Siegel domains. The main object of our study concerns weighted mixed norm Bergman spaces on homogeneous Siegel domains of type II. These problems include: sampling, atomic decomposition, duality, boundary values, boundedness of the Bergman projectors. Our analysis include the Hardy spaces, and suitable generalizations of the classical Bloch and Dirichlet spaces. One of the main novelties in this work is the generality of the domains under consideration, that is, homogeneous Siegel domains, extending many results from the more particular cases of the upper half-plane, Siegel domains of tube type over irreducible cones, or symmetric, irreducible Siegel domains of type II.

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齐次Siegel域上的全纯函数空间

我们研究齐次Siegel域上全纯函数空间的几个连通问题。我们研究的主要对象是II型齐次Siegel域上的加权混合范数Bergman空间。这些问题包括：采样，原子分解，对偶，边值，Bergman投影的有界性。我们的分析包括Hardy空间，以及经典Bloch和Dirichlet空间的适当推广。这项工作的一个主要新颖之处是所考虑的域的一般性，即齐次西格尔域，扩展了上半平面、不可约锥上的管型西格尔域或II型对称不可约西格尔域的许多特殊情况的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.