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Weighted composition operators on weighted Bergman and Dirichlet spaces

Part of: Special classes of linear operators

Published online by Cambridge University Press:  28 April 2022

Kobra Esmaeili Open the ORCID record for Kobra Esmaeili [Opens in a new window]  and
Karim Kellay
Kobra Esmaeili*
Affiliation:
Faculty of Engineering, Ardakan University, Ardakan, Yazd 89518-95491, Iran
Karim Kellay
Affiliation:
CNRS, Bordeaux INP, IMB, UMR 5251, University of Bordeaux, Talence 33405, France e-mail: kkellay@math.u-bordeaux.fr
*
e-mail: esmaeili@ardakan.ac.ir
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Abstract

We study the boundedness and compactness of weighted composition operators acting on weighted Bergman spaces and weighted Dirichlet spaces by using the corresponding Carleson measures. We give an estimate for the norm and the essential norm of weighted composition operators between weighted Bergman spaces as well as the composition operators between weighted Hilbert spaces.

Keywords

Weighted composition operatorsboundednesscompactnessCarleson measuresBergman spacesDirichlet spacesweighted Hilbert spaces

MSC classification

Primary: 47B33: Composition operators
Secondary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Type
Article
Information
Canadian Mathematical Bulletin , Volume 66 , Issue 1 , March 2023 , pp. 286 - 302
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

The research of the first author is supported by a grant by the Embassy of France in Iran. The research of the second author is partially supported by the project ANR-18-CE40-0035.

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