Supnorm and f-Holder estimates for di-bar on convex domains of general type in C^2

TL;DR

This paper establishes supnorm and F-Holder estimates for solutions to the di-bar-equation on convex domains of general type in C^2, including many infinite type examples, advancing the understanding of complex analysis in these settings.

Contribution

It provides new supnorm and F-Holder estimates for the di-bar-equation on a broad class of convex domains of general type in C^2, including infinite type cases.

Findings

Established supnorm estimates for di-bar solutions.

Derived F-Holder estimates applicable to infinite type domains.

Extended analysis to convex domains of general type in C^2.

Abstract

In this paper, we study supnorm and modified H\"{o}lder estimates for the integral solution of the di-bar-equation on a class of convex domains of general type in $\C^2$ that includes many infinite type examples.