Composition operator and Sobolev-Lorentz spaces

Abstract

Let Omega, Omega' subset of R-n be domains and let f: Omega -> Omega' be a homeomorphism. We show that if the composition operator T-f : u -> u o f maps the Sobolev-Lorentz space WLn,q(Omega') to WLn,q(Omega) for some q not equal n then f must be a locally bilipschitz mapping.

Keywords

• composition operator
• Lorentz space
• Sobolev-Lorentz space