Boundedness and compactness of Hausdorff operators on Fock spaces

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2024-01-25 DOI:10.1090/tran/9133

Óscar Blasco, Antonio Galbis

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引用次数: 0

Abstract

We obtain a complete characterization of the bounded Hausdorff operators acting on a Fock space F α p F^p_\alpha and taking its values into a larger one F α q , 0 > p ≤ q ≤ ∞ F^q_\alpha ,\ 0 > p \leq q \leq \infty , as well as some necessary or sufficient conditions for a Hausdorff operator to transform a Fock space into a smaller one. Some results are written in the context of mixed norm Fock spaces. Also the compactness of Hausdorff operators on a Fock space is characterized. The compactness result for Hausdorff operators on the Fock space F α ∞ F^\infty _\alpha is extended to more general Banach spaces of entire functions with weighted sup norms defined in terms of a radial weight and conditions for the Hausdorff operators to become p p -summing are also included.

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福克空间上豪斯多夫算子的有界性和紧凑性

我们得到了作用于Fock空间F α p F^p_\alpha 并将其值转化为更大的F α q , 0 > p ≤ q ≤ ∞ F^q_\alpha ,\ 0 > p \leq q \leq \infty 的有界Hausdorff算子的完整描述，以及Hausdorff算子将Fock空间转化为更小的Fock空间的一些必要或充分条件。一些结果是在混合规范 Fock 空间的背景下写出的。此外，还描述了福克空间上豪斯多夫算子的紧凑性。福克空间 F α ∞ F^\infty _\alpha 上豪斯多夫算子的紧凑性结果被扩展到更一般的全函数巴纳赫空间，其加权超规范是以径向权重定义的，豪斯多夫算子成为 p p - 和的条件也包括在内。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.