Tangential Lipschitz Gain for Holomorphic Functions on Domains of Finite Type

TL;DR

This paper investigates how holomorphic Lipschitz functions on finite type domains exhibit increased regularity in tangential directions near the boundary, with explicit descriptions based on the defining function.

Contribution

It provides an explicit characterization of the tangential Lipschitz gain for holomorphic functions near finite type boundary points.

Findings

Explicit formula for Lipschitz gain in tangential directions

Description of regularity improvement based on boundary defining function

Analysis focused on finite type boundary points

Abstract

Functions that are holomorphic and Lipschitz in a smoothly bounded domain enjoy a gain in the order of Lipschitz regularity in the complex tangential directions near the boundary. We describe this gain explicitly in terms of the defining function near points of finite type in the boundary.