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arXiv · 2507.09154

A class of linear operators on Bergman spaces

Zengjian Lou·Antti Rasila·Senhua Zhu
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Abstract

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

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Zengjian Lou, Antti Rasila, Senhua Zhu. 2025-07-12. A class of linear operators on Bergman spaces. https://arxiv.org/abs/2507.09154

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