Cesàro-type operators associated with Borel measures on the unit disc acting on some Hilbert spaces of analytic functions

Given a complex Borel measure μ on the unit disc D={z∈C:|z|−1). Among other results, we prove that, if we set Fμ(z)=∑n=0∞μnzn (z∈D), then Cμ is bounded on H2 or on Aα2 if and only if Fμ belongs to the mean Lipschitz space Λ1/22. We prove also that Cμ is a Hilbert-Schmidt operator on H2 if and only i...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2023-10, Vol.526 (2), p.127287, Article 127287
Main Authors: Galanopoulos, Petros, Girela, Daniel, Merchán, Noel
Format: Article
Language:English
Subjects:
Cesàro-type operators
Hardy spaces
Hilbert-Schmidt operators
Mean Lipschitz spaces
Weighted Bergman spaces
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Summary:Given a complex Borel measure μ on the unit disc D={z∈C:|z|−1). Among other results, we prove that, if we set Fμ(z)=∑n=0∞μnzn (z∈D), then Cμ is bounded on H2 or on Aα2 if and only if Fμ belongs to the mean Lipschitz space Λ1/22. We prove also that Cμ is a Hilbert-Schmidt operator on H2 if and only if Fμ belongs to the Dirichlet space D, and that Cμ is a Hilbert-Schmidt operator on Aα2 if and only if Fμ belongs to the Dirichlet-type space D−1−α2.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127287