Weighted Bergman Projection on the Hartogs Triangle

Abstract

We prove the $L^p$ regularity of the weighted Bergman projection on the Hartogs triangle, where the weights are powers of the distance to the singularity at the boundary. The restricted range of $p$ is proved to be sharp. By using a two-weight inequality on the upper half plane with Muckenhoupt weights, we can consider a slightly wider class of weights.

The article has been revised. There are 23 pages in total

References in corpus (4)

• Irregularity of the Bergman projection on worm domains in C^n
• The Bergman kernel and projection on non-smooth worm domains
• The $L^p$ boundedness of the Bergman projection for a class of bounded Hartogs domains
• $L^p$ Regularity of Weighted Bergman Projections

Cited by in corpus (6)

• Weighted estimates for the Bergman projection on the Hartogs triangle
• Weighted Bergman Projections on the Hartogs Triangle: Exponential Decay
• Weighted Sobolev regularity of the Bergman projection on the Hartogs triangle
• $L^p$ Mapping Properties for the Cauchy-Riemann Equations on Lipschitz Domains Admitting Subelliptic Estimates
• (Ir-)regularity of canonical projection operators on some weakly pseudoconvex domains
• $L^p$ regularity of weighted Bergman projection on Fock-Bargmann-Hartogs domain