Homeomorphic Extensions in Bi-Orlicz-Sobolev Spaces

TL;DR

This paper characterizes which circle homeomorphisms extend to the disk as bi-Orlicz-Sobolev functions, generalizing classical Sobolev criteria to a more flexible Orlicz setting.

Contribution

It provides a complete characterization of circle homeomorphisms extendable to bi-Orlicz-Sobolev spaces, extending classical Sobolev results to the Orlicz framework.

Findings

Complete characterization of circle homeomorphisms extension criteria

Generalization of Sobolev criteria to Orlicz spaces

Extension results applicable to bi-Orlicz-Sobolev spaces

Abstract

We provide a complete characterization of those self-homeomorphisms of the unit circle that admit homeomorphic extensions to the unit disk belonging to bi--Orlicz--Sobolev spaces. Our results generalize classical criteria from the Sobolev setting to the more flexible Orlicz framework.