Weighted estimates for solutions of the $\partial$ -equation for lineally convex domains of finite type and applications to weighted bergman projections

TL;DR

This paper establishes sharp weighted estimates for solutions of the $ar{ ext{d}}$-equation in lineally convex domains of finite type, extending regularity results for weighted Bergman projections to broader weights.

Contribution

It provides new weighted estimates for the $ar{ ext{d}}$-equation in lineally convex domains, enabling extension of regularity results for weighted Bergman projections beyond convex domains.

Findings

Sharp weighted estimates in Lp spaces with boundary distance weights

Extension of regularity results for weighted Bergman projections

Broader applicability to general weights in complex analysis

Abstract

In this paper we obtain sharp weighted estimates for solutions of the $\partial$-equation in a lineally convex domains of finite type. Precisely we obtain estimates in spaces of the form L p ({\Omega},$\delta$ $\gamma$), $\delta$ being the distance to the boundary, with gain on the index p and the exponent $\gamma$. These estimates allow us to extend the L p ({\Omega},$\delta$ $\gamma$) and lipschitz regularity results for weighted Bergman projection obtained in [CDM14b] for convex domains to more general weights.