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

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.

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

References in corpus (8)

• Lectures on 0/1-polytopes
• The Bergman projection on fat Hartogs triangles: L^p boundedness
• Bergman subspaces and subkernels: Degenerate $L^p$ mapping and zeroes
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• Bergman Kernels of Elementary Reinhardt Domains
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Cited by in corpus (4)

• Projections onto $L^p$-Bergman spaces of Reinhardt Domains
• $L^p$ regularity of the Bergman projection on the symmetrized polydisc
• The weighted Bergman spaces and complex reflection groups
• Nonabelian ramified coverings and $L^p$-boundedness of Bergman projections in ${\mathbb{C}}^2$