The Hadamard–Bergman Convolution on the Half-Plane

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-18 DOI:10.1007/s00041-024-10097-9

Alexey Karapetyants, Armen Vagharshakyan

引用次数: 0

Abstract

We introduce the Hadamard–Bergman convolution on the half-plane. We show that it exists in terms of the Hadamard product and it is commutative on the Bergman space (more appropriately called the Bergman–Jerbashian space) in the half-plane. Further, we explore mapping properties of the generalized Bergman-type operators with exponential weights in weighted Bergman spaces in the half-plane. Finally, we deduce sharp inclusions for weighted Bergman spaces, from corresponding Sobolev-type inequalities.

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半平面上的哈达玛-伯格曼卷积

我们介绍半平面上的哈达玛-伯格曼卷积。我们证明了它存在于哈达玛积，并且在半平面上的伯格曼空间（更恰当地称为伯格曼-杰巴希安空间）上是交换的。此外，我们还探讨了半平面内加权伯格曼空间中具有指数权的广义伯格曼型算子的映射性质。最后，我们从相应的索博列夫型不等式中推导出加权伯格曼空间的尖锐夹杂。

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.