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A class of linear operators on Bergman spaces | Synapse

April 22, 2026Complex Analysis and Operator Theory0 citationsOpen Access

A class of linear operators on Bergman spaces

ZLZengjian Lou ARAntti Rasila SZSenhua ZhuShantou University

Key Points

The aim is to investigate the boundedness and compactness conditions of linear operators on Bergman spaces.
Analyzed linear operator S on L^p_a(dA_α) for 0<p<∞
Derived sufficient and necessary conditions for compactness in the interval 1<p<∞
Identified specific conditions for the boundedness of the operator S
Established new insights that relax earlier assumptions from previous studies by J. Miao and D. Zheng

Abstract

We study the boundedness of the linear operator S on L^p₀ (dA) ~ (0<p<). In particular, we obtain a sufficient and necessary condition for the compactness of the linear operator S on L^p₀ (dA) ~ (1<p<). Our results weaken the assumptions of earlier results of J. Miao and D. Zheng in a certain sense.

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Cite This Study

Lou et al. (Mon,) studied this question.

synapsesocial.com/papers/69e865926e0dea528ddea054 https://doi.org/https://doi.org/10.1007/s11785-026-01947-z