A berndtsson-Andersson operator solving \bar\partial-equation with W^\alpha-estimates on convex domains of finite type

TL;DR

This paper introduces a method using the Berndtsson-Andersson operator and Bergman metric to solve the ar ext{d} equation on convex finite type domains, providing norm estimates based on Carleson conditions.

Contribution

It develops a new approach combining the Berndtsson-Andersson operator with Bergman metric to obtain ar ext{d} solutions with Carleson norm estimates on convex finite type domains.

Findings

Successfully solves ar ext{d} equation with Carleson norm estimates

Establishes bounds for solutions in terms of Carleson norms

Extends techniques to convex domains of finite type

Abstract

In this article, we use a Berndtsson-Andersson operator and the Bergman metric in order to solve the $\bar\partial$ equation on convex domains of finite type for forms satisifying a Carleson condition and get norm estimates of the solution in term of the Carleson norm.