积分估计与正规权Dirichlet空间上的Cesàro型算子

唐鹏程, 吕睿昕, 张学军

数学学报 ›› 2021, Vol. 64 ›› Issue (4) : 627-636.

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PDF(438 KB)
数学学报 ›› 2021, Vol. 64 ›› Issue (4) : 627-636. DOI: 10.12386/A2021sxxb0054
论文

积分估计与正规权Dirichlet空间上的Cesàro型算子

    唐鹏程, 吕睿昕, 张学军
作者信息 +

An Integral Estimate and Cesàro Type Operators on Normal Weight Dirichlet Spaces

    Peng Cheng TANG, Rui Xin LV, Xue Jun ZHANG
Author information +
文章历史 +

摘要

μ是[0,1)上的一个正规函数,本文给出了正规权测度下单位球内单变点球体积分的部分情况下的双向估计,在特殊情况下给出了所有指标情形的双向估计.作为一个应用,本文还给出了一些情况下正规权Dirichlet空间上Cesàro型算子有界或紧的充要条件.

Abstract

Let μ be a normal function on[0, 1). In this paper, the authors give the bidirectional estimates of the volume integral of a single variable point in the unit ball under the normal weight measure in some cases, and give the bidirectional estimates for all indicators in special cases. As an application, the authors give some necessary and sufficient conditions for the boundedness or compactness of Cesàro type operator on normal weight Dirichlet spaces.

关键词

积分估计 / 正规权测度 / 正规权Dirichlet空间 / Cesà / ro型算子 / 有界性和紧性

Key words

integral estimate / normal weight measure / normal weight Dirichlet space / Cesà / ro type operator / boundedness and compactness

引用本文

导出引用
唐鹏程, 吕睿昕, 张学军. 积分估计与正规权Dirichlet空间上的Cesàro型算子. 数学学报, 2021, 64(4): 627-636 https://doi.org/10.12386/A2021sxxb0054
Peng Cheng TANG, Rui Xin LV, Xue Jun ZHANG. An Integral Estimate and Cesàro Type Operators on Normal Weight Dirichlet Spaces. Acta Mathematica Sinica, Chinese Series, 2021, 64(4): 627-636 https://doi.org/10.12386/A2021sxxb0054

参考文献

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基金

国家自然科学基金资助项目(11942109);湖南省研究生科研创新项目(CX2018B286)

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