Composition operators on Hardy-Sobolev spaces and $BMO$-quasiconformal mappings

TL;DR

This paper investigates how $BMO$-quasiconformal mappings induce bounded composition operators between Hardy-Sobolev and Sobolev spaces, utilizing duality principles to establish their boundedness.

Contribution

It demonstrates that $BMO$-quasiconformal mappings generate bounded composition operators from Hardy-Sobolev spaces to Sobolev spaces, connecting geometric mappings with functional analysis.

Findings

$BMO$-quasiconformal mappings induce bounded composition operators

Duality of Hardy and $BMO$-spaces is key to the proof

Boundedness links geometric mappings to functional spaces

Abstract

In this paper we consider composition operators on Hardy-Sobolev spaces in connections with $BMO$-quasiconformal mappings. Using the duality of Hardy spaces and $BMO$-spaces we prove that $BMO$-quasiconformal mappings generate bounded composition operators from Hardy-Sobolev spaces to Sobolev spaces.