Hardy spaces and unbounded quasidisks

TL;DR

This paper investigates the maximal exponent range for which analytic functions in the unit disk map into a given domain, providing estimates for unbounded quasidisks.

Contribution

It offers new estimates of the maximal exponent for functions mapping into unbounded quasidisks, extending understanding of Hardy spaces and quasidisk geometry.

Findings

Derived bounds for the maximal exponent h in unbounded quasidisks

Extended Hardy space theory to unbounded quasidisks

Provided new geometric estimates for quasidisks

Abstract

We study the maximal number $0\le h\le+\infty$ for a given plane domain $\Omega$ such that $f\in H^p$ whenever $p<h$ and $f$ is analytic in the unit disk with values in $\Omega.$ One of our main contributions is an estimate of $h$ for unbounded $K$-quasidisks.