Geodesic
Composition operator and Sobolev–Lorentz spaces $WL^{n,q}$
Stanislav Hencl 1   ; Luděk Kleprlík 1   ; Jan Malý 1
1 Department of Mathematical Analysis Charles University Sokolovská 83 186 00 Praha, Czech Republic
Studia Mathematica, Tome 221 (2014) no. 3, pp. 197-208 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm221-3-1
Keywords: omega omega subset mathbb domains colon omega omega homeomorphism composition operator colon mapsto circ maps sobolev lorentz space omega omega neq locally bilipschitz mapping

Stanislav Hencl  1   ; Luděk Kleprlík  1   ; Jan Malý  1

1 Department of Mathematical Analysis Charles University Sokolovská 83 186 00 Praha, Czech Republic 
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Stanislav Hencl; Luděk Kleprlík; Jan Malý. Composition operator and Sobolev–Lorentz spaces $WL^{n,q}$. Studia Mathematica, Tome 221 (2014) no. 3, pp. 197-208. doi: 10.4064/sm221-3-1

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