Restricted type estimates on the Bergman projection of some singular domains

Abstract

We obtain (weighted) restricted type estimates for the Bergman projection operator on monomial polyhedra, a class of domains generalizing the Hartogs triangle. From these estimates, we recapture $L^p$ boundedness results of the Bergman projection on these domains. On some monomial polyhedra, we also discover that the Bergman projection could fail to be of weak type $(q_{\ast },q_{\ast })$ where $q_{\ast }$ is the right endpoint of the interval of $L^p$-regularity of the domain.