A class of linear operators on Bergman spaces

We study the boundedness of the linear operator $S$ on $L^{p}_{a}(dA_α)$ $(0<p<\infty)$. In particular, we obtain a sufficient and necessary condition for the compactness of the linear operator $S$ on $L^{p}_{a}(dA_α)$ $(1<p<\infty)$. Our results weaken the assumptions of earlier results of J. Miao and D. Zheng in a certain sense.

Publication Details

Journal
ArXiv.org
Published
2025-07-12
Primary Topic
Holomorphic and Operator Theory
Type
article
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article

A class of linear operators on Bergman spaces

ArXiv.org
Holomorphic and Operator Theory
article

A class of linear operators on Bergman spaces

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Abstract

We study the boundedness of the linear operator $S$ on $L^{p}_{a}(dA_α)$ $(0<p<\infty)$. In particular, we obtain a sufficient and necessary condition for the compactness of the linear operator $S$ on $L^{p}_{a}(dA_α)$ $(1<p<\infty)$. Our results weaken the assumptions of earlier results of J. Miao and D. Zheng in a certain sense.

ArXiv.org
Openalex Percentile: Top 39%
Holomorphic and Operator Theory
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A class of linear operators on Bergman spaces · ArXiv.org (2025) | TGRS Research Map | TGRS