H\"{o}lder estimates for Cauchy-Type Integrals and proper holomorphic mappings of symmetric products

TL;DR

This paper establishes Hölder space estimates for Cauchy-type integrals and explores boundary regularity of proper holomorphic maps between symmetric products of planar domains, advancing understanding of complex analysis in these contexts.

Contribution

It provides new Hölder estimates for Cauchy-type integrals and analyzes boundary regularity of holomorphic maps between symmetric products, which was previously less understood.

Findings

Hölder estimates for Cauchy-type integral operators

Boundary regularity results for proper holomorphic maps

Enhanced understanding of symmetric product mappings

Abstract

We prove estimates in H\"{o}lder spaces for some Cauchy-type integral operators representing holomorphic functions in Cartesian and symmetric products of planar domains. As a consequence, we obtain information on the boundary regularity in H\"{o}lder spaces of proper holomorphic maps between symmetric products of planar domains.