Composition operator and Sobolev–Lorentz spaces
Tom 221 / 2014
Studia Mathematica 221 (2014), 197-208
MSC: Primary 30C65; Secondary 46E35, 46E30.
DOI: 10.4064/sm221-3-1
Streszczenie
Let \Omega,\Omega'\subset\mathbb R^n be domains and let f\colon\Omega\to\Omega' be a homeomorphism. We show that if the composition operator T_f\colon u\mapsto u\circ f maps the Sobolev–Lorentz space WL^{n,q}(\Omega') to WL^{n,q}(\Omega) for some q\neq n then f must be a locally bilipschitz mapping.
