Dyadic decomposition of convex domains of finite type and applications

TL;DR

This paper develops a dyadic framework for convex finite type domains to establish weighted norm estimates for the Bergman projection, providing new proofs and extending to vector-valued and modular inequalities.

Contribution

It introduces a dyadic structure on convex domains of finite type and applies it to derive weighted estimates for the Bergman projection, including new proofs and extensions.

Findings

Weighted norm estimates for the Bergman projection established

Alternative proof of L^p boundedness provided

Extended results to vector-valued and modular inequalities

Abstract

In this paper, we introduce a dyadic structure on convex domains of finite type via the so-called dyadic flow tents. This dyadic structure allows us to establish weighted norm estimates for the Bergman projection $P$ on such domains with respect to Muckenhoupt weights. In particular, this result gives an alternative proof of the $L^p$ boundedness of $P$. Moreover, using extrapolation, we are also able to derive weighted vector-valued estimates and weighted modular inequalities for the Bergman projection.