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

Stanislav Hencl, Luděk Kleprlík, and Jan Malý. "Composition operator and Sobolev-Lorentz spaces $WL^{n,q}$." Studia Mathematica 221.3 (2014): 197-208. <http://eudml.org/doc/285499>.

@article{StanislavHencl2014,
abstract = {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 $WL^\{n,q\}(Ω^\{\prime \})$ to $WL^\{n,q\}(Ω)$ for some q ≠ n then f must be a locally bilipschitz mapping.},
author = {Stanislav Hencl, Luděk Kleprlík, Jan Malý},
journal = {Studia Mathematica},
keywords = {quasiconformal mapping; composition operator; Lorentz space; Sobolev-Lorentz space},
language = {eng},
number = {3},
pages = {197-208},
title = {Composition operator and Sobolev-Lorentz spaces $WL^\{n,q\}$},
url = {http://eudml.org/doc/285499},
volume = {221},
year = {2014},
}

TY - JOUR
AU - Stanislav Hencl
AU - Luděk Kleprlík
AU - Jan Malý
TI - Composition operator and Sobolev-Lorentz spaces $WL^{n,q}$
JO - Studia Mathematica
PY - 2014
VL - 221
IS - 3
SP - 197
EP - 208
AB - 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 $WL^{n,q}(Ω^{\prime })$ to $WL^{n,q}(Ω)$ for some q ≠ n then f must be a locally bilipschitz mapping.
LA - eng
KW - quasiconformal mapping; composition operator; Lorentz space; Sobolev-Lorentz space
UR - http://eudml.org/doc/285499
ER -