Inner Functions in certain Hardy-Sobolev Spaces

TL;DR

This paper characterizes inner functions in specific Hardy-Sobolev spaces with derivatives in Hardy spaces, using their mapping properties and zero distribution.

Contribution

It provides a new description of inner functions in Hardy-Sobolev spaces based on their geometric zero distribution and mapping characteristics.

Findings

Inner functions with derivatives in H^p are characterized by their zero distribution.

Mapping properties of these inner functions are linked to their derivative behavior.

The results extend understanding of Hardy-Sobolev space functions for 1/2<p<1.

Abstract

For $1/2<p<1$, a description of inner functions whose derivative is in the Hardy space $H^p$ is given in terms of either their mapping properties or the geometric distribution of their zeros.