Weighted estimates for the Bergman projection on the Hartogs triangle

Abstract

We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on the Hartogs triangle. The estimates of the operator norm are in terms of a Bekoll\'e-Bonami type constant. As an application of the results obtained, we give, for example, an upper bound for the $L^p$ norm of the Bergman projection on the generalized Hartogs triangle $\mathbb H_{m/n}$ in $\mathbb C^2$.