Composition operator and Sobolev-Lorentz spaces WLn,q
Stanislav Hencl ; Luděk Kleprlík ; Jan Malý
Studia Mathematica, Tome 223 (2014), p. 197-208 / Harvested from The Polish Digital Mathematics Library
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Let Ω,Ω’ ⊂ ℝⁿ be domains and let f: Ω → Ω’ be a homeomorphism. We show that if the composition operator Tf:u↦u∘f maps the Sobolev-Lorentz space WLn,q(Ω') to WLn,q(Ω) for some q ≠ n then f must be a locally bilipschitz mapping.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:285499 
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Stanislav Hencl; Luděk Kleprlík; Jan Malý. Composition operator and Sobolev-Lorentz spaces $WL^{n,q}$
            . Studia Mathematica, Tome 223 (2014) pp. 197-208. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm221-3-1/