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

TL;DR

This paper establishes precise $L^p$-boundedness ranges for the Bergman projection on a broad class of Reinhardt domains, using a transformation law relating quotient domains and analyzing how domain complexity affects these ranges.

Contribution

It introduces a general transformation law linking $L^p$-boundedness on a domain and its quotient, and determines how domain complexity influences the $L^p$ bounds for the Bergman projection.

Findings

Sharp $L^p$-boundedness ranges are obtained for the Bergman projection.

The $L^p$ range shrinks as the domain's complexity increases.

A transformation law relates $L^p$-boundedness between a domain and its quotient.

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.