Hardy spaces and unbounded 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.

11 pages