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

Chase Bender; Debraj Chakrabarti; Luke D. Edholm; Meera Mainkar

doi:10.4153/S0008414X21000079

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

Complex Variables 2021-11-16 v3

Authors: Chase Bender , Debraj Chakrabarti , Luke D. Edholm , Meera Mainkar

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Abstract

We obtain sharp ranges of $L^p$ -boundedness for domains in a wide class of Reinhardt domains representable as sub-level 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 projection $L^p$-boundedness Reinhardt domains quotient domains transformation law

Cite

@article{arxiv.2004.02598,
  title  = {$L^p$-regularity of the Bergman projection on quotient domains},
  author = {Chase Bender and Debraj Chakrabarti and Luke D. Edholm and Meera Mainkar},
  journal= {arXiv preprint arXiv:2004.02598},
  year   = {2021}
}

Comments

New main theorem and two new co-authors. The new results are applicable to a much more general class of domains

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

Abstract

Keywords

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