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 Bekollé-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 ${\mathbb{C}}^2$.

arXiv comment27 pages, an issue about our sharp example and sharp estimate has been fixed. Accepted in the Journal of Functional Analysis

References in corpus (4)

• The Bergman projection on fat Hartogs triangles: L^p boundedness
• Bergman subspaces and subkernels: Degenerate $L^p$ mapping and zeroes
• Irregularity of the Bergman projection on worm domains in C^n
• Weighted Bergman Projection on the Hartogs Triangle

Cited by in corpus (6)

• Weak-type estimates for the Bergman projection on the polydisc and the Hartogs triangle
• Bekollé-Bonami estimates on some pseudoconvex domains
• Dyadic Carleson embedding and sparse domination of weighted composition operators on strictly pseudoconvex domains
• Bergman projection on the symmetrized bidisk
• (Ir-)regularity of canonical projection operators on some weakly pseudoconvex domains
• Sparse domination of weighted composition operators on weighted Bergman spaces in the upper half-plane