Hausdorff–Berezin and Hausdorff–Zhu Operators on Bidisc

The article introduces and studies Hausdorff–Berezin and Hausdorff–Zhu type operators on bidisc. These operators are natural generalization of the Berezin transform and some other classical operators of mathematical physics. Sufficient and necessary conditions for boundedness of such operators in th...

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Bibliographic Details
Published inLobachevskii journal of mathematics Vol. 45; no. 12; pp. 6094 - 6110
Main Authors Grigorian, V. A., Karapetyants, A. N.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2024
Subjects
Algebra
Analysis
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Berezin transform
2010 Mathematics Subject Classification: 47G10; 47B38; 46E30
Hausdorff operators
Haar measure
Möbius group
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Summary:The article introduces and studies Hausdorff–Berezin and Hausdorff–Zhu type operators on bidisc. These operators are natural generalization of the Berezin transform and some other classical operators of mathematical physics. Sufficient and necessary conditions for boundedness of such operators in the mixed norm weighted Lebesgue type spaces are given. We also study the question of identity approximations by such operators in the mixed norm weighted Lebesgue type spaces on bidisc.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224607392