Composition operator and Sobolev-Lorentz spaces $WL^{n,q}$

• Autorzy: Stanislav Hencl , Luděk Kleprlík , Jan Malý
• Języki publikacji: EN

Abstrakty

EN

Let Ω,Ω' ⊂ ℝⁿ be domains and let f: Ω → Ω' be a homeomorphism. We show that if the composition operator $T_{f}: u ↦ u∘ f$ maps the Sobolev-Lorentz space $WL^{n,q}(Ω')$ to $WL^{n,q}(Ω)$ for some q ≠ n then f must be a locally bilipschitz mapping.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 30C65: Quasiconformal mappings in 𝐑 n , other generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 221
• Numer: 3
• Strony: 197-208

Daty

wydano

2014

Twórcy

autor

Stanislav Hencl

• Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 00 Praha, Czech Republic

autor

Luděk Kleprlík

• Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 00 Praha, Czech Republic

autor

Jan Malý

• Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 00 Praha, Czech Republic

Identyfikatory

DOI

10.4064/sm221-3-1