从混合模空间到Zygmund空间的Volterra型复合算子

刘永民, 刘浩

数学学报 ›› 2011, Vol. 54 ›› Issue (3) : 381-396.

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数学学报 ›› 2011, Vol. 54 ›› Issue (3) : 381-396. DOI: 10.12386/A2011sxxb0039
论文

从混合模空间到Zygmund空间的Volterra型复合算子

    刘永民, 刘浩
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Volterra-Type Composition Operators from Mixed Norm Spaces to Zygmund Spaces

    Yong Min LIU, Hao LIU
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摘要

本文利用混合模空间 H(p, q, Φ) 中函数的高阶导数的估计,通过构造一些新的检验函数, 运用解析函数的性质与算子理论,给出了从混合模空间 H(p, q, Φ) 到 Zygmund 空间的 Volterra 型复合算子的有界性和紧性的特征, 获得了若干个充要条件.  

Abstract

In this paper, using the estimate of the higher order derivative of the function in mixed norm spaces, the properties of the analytic function and operator theory, the authors characterize the boundedness and compactness of the Volterra-type composition operator from mixed norm spaces H(p, q, Φ) to Zygmund spaces by means of constructing some test functions, and some necessary and sufficient conditions of the Volterra-type composition operators to be bounded and compact are obtained.  

关键词

混合模空间 / Zygmund 空间 / Volterra 型复合算子

Key words

mixed norm space / Zygmund space / Volterra-type composition operators

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刘永民, 刘浩. 从混合模空间到Zygmund空间的Volterra型复合算子. 数学学报, 2011, 54(3): 381-396 https://doi.org/10.12386/A2011sxxb0039
Yong Min LIU, Hao LIU. Volterra-Type Composition Operators from Mixed Norm Spaces to Zygmund Spaces. Acta Mathematica Sinica, Chinese Series, 2011, 54(3): 381-396 https://doi.org/10.12386/A2011sxxb0039

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基金

国家自然科学基金资助项目(10471039);江苏省普通高校自然科学研究计划资助项目(06KJD110175,07KJB110115)

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