Derivatives characterization of Bergman-Orlicz spaces, boundedness and compactness of Cesàro-type operator

Benoît F. Sehba

doi:10.1016/j.bulsci.2022.103193

Derivatives characterization of Bergman-Orlicz spaces, boundedness and compactness of Cesàro-type operator

Benoît F. Sehba

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

It is well known that a function is in a Bergman space of the unit ball if and only if it satisfies some Hardy-type inequalities. We extend this fact to Bergman-Orlicz spaces. We then completely characterize symbols of bounded or compact Cesàro-type operators on Bergman-Orlicz spaces, extending known results for classical weighted Bergman spaces.

Original language	English
Article number	103193
Journal	Bulletin des Sciences Mathematiques
Volume	180
DOIs	https://doi.org/10.1016/j.bulsci.2022.103193
Publication status	Published - Nov 2022

Keywords

Bergman-Orlicz space
Bloch space
Cesàro operator

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10.1016/j.bulsci.2022.103193

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abstract = "It is well known that a function is in a Bergman space of the unit ball if and only if it satisfies some Hardy-type inequalities. We extend this fact to Bergman-Orlicz spaces. We then completely characterize symbols of bounded or compact Ces{\`a}ro-type operators on Bergman-Orlicz spaces, extending known results for classical weighted Bergman spaces.",

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N2 - It is well known that a function is in a Bergman space of the unit ball if and only if it satisfies some Hardy-type inequalities. We extend this fact to Bergman-Orlicz spaces. We then completely characterize symbols of bounded or compact Cesàro-type operators on Bergman-Orlicz spaces, extending known results for classical weighted Bergman spaces.

AB - It is well known that a function is in a Bergman space of the unit ball if and only if it satisfies some Hardy-type inequalities. We extend this fact to Bergman-Orlicz spaces. We then completely characterize symbols of bounded or compact Cesàro-type operators on Bergman-Orlicz spaces, extending known results for classical weighted Bergman spaces.

KW - Bergman-Orlicz space

KW - Bloch space

KW - Cesàro operator

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VL - 180

JO - Bulletin des Sciences Mathematiques

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M1 - 103193

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Derivatives characterization of Bergman-Orlicz spaces, boundedness and compactness of Cesàro-type operator

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Keywords

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