Peak functions and boundary behaviour of holomorphically invariant distances on strictly pseudoconvex domains

TL;DR

This paper extends approximation theorems for bounded holomorphic functions on strictly pseudoconvex domains and provides uniform boundary estimates for the Kobayashi and Carathéodory distances, enhancing understanding of their boundary behaviour.

Contribution

It introduces a parameter version of the Graham-Kerzman approximation theorem and applies it to derive boundary estimates for invariant distances.

Findings

Established a parameterized approximation theorem for holomorphic functions

Derived uniform boundary estimates for Kobayashi and Carathéodory pseudodistances

Enhanced understanding of boundary behaviour of invariant distances on pseudoconvex domains

Abstract

We give a parameter version of Graham-Kerzman approximation theorem for bounded holomorphic functions on strictly pseudoconvex domains. As an application, we present some uniform estimates for the boundary behaviour of the Kobayashi and Carath\'eodory pseudodistences on such domains.