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$L^p$-regularity of the Bergman projection on quotient domains

Part of: Holomorphic functions of several complex variables

Published online by Cambridge University Press:  08 February 2021

Chase Bender ,
Debraj Chakrabarti ,
Luke Edholm  and
Meera Mainkar
Chase Bender*
Affiliation:
Department of Mathematics, Central Michigan University, Mt Pleasant, MI48859, USA e-mail: chakr2d@cmich.edumaink1m@cmich.edu URL: http://people.cst.cmich.edu/chakr2d
Debraj Chakrabarti
Affiliation:
Department of Mathematics, Central Michigan University, Mt Pleasant, MI48859, USA e-mail: chakr2d@cmich.edumaink1m@cmich.edu URL: http://people.cst.cmich.edu/chakr2d
Luke Edholm
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI48109, USA e-mail: edholm@umich.edu
Meera Mainkar
Affiliation:
Department of Mathematics, Central Michigan University, Mt Pleasant, MI48859, USA e-mail: chakr2d@cmich.edumaink1m@cmich.edu URL: http://people.cst.cmich.edu/chakr2d
*
bende1cc@cmich.edu
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Abstract

We obtain sharp ranges of $L^p$ -boundedness for domains in a wide class of Reinhardt domains representable as sublevel sets of monomials, by expressing them as quotients of simpler domains. We prove a general transformation law relating $L^p$ -boundedness on a domain and its quotient by a finite group. The range of p for which the Bergman projection is $L^p$ -bounded on our class of Reinhardt domains is found to shrink as the complexity of the domain increases .

Keywords

Bergman spacesBergman projectionReinhardt domainsGeneralized Hartogs triangle

MSC classification

Primary: 32A36: Bergman spaces
Type
Article
Information
Canadian Journal of Mathematics , Volume 74 , Issue 3 , June 2022 , pp. 732 - 772
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Copyright
© Canadian Mathematical Society 2021

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Footnotes

Chase Bender was supported by a Student Research and Creative Endeavors grant from Central Michigan University.

Debraj Chakrabarti was partially supported by National Science Foundation grant DMS-1600371.

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