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

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.