Open Access
Fall 2012 Composition of $q$-quasiconformal mappings and functions in Orlicz–Sobolev spaces
Stanislav Hencl, Luděk Kleprlík
Illinois J. Math. 56(3): 931-955 (Fall 2012). DOI: 10.1215/ijm/1391178556


Let $\Omega\subset\mathbb{R}^{n}$, $q\geq n$ and $\alpha\geq0$ or $1<q\leq n$ and $\alpha\leq0$. We prove that the composition of $q$-quasiconfomal mapping $f$ and function $u\in WL^{q}\log^{\alpha}L_{\operatorname{loc}}(f(\Omega))$ satisfies $u\circ f\in WL^{q}\log^{\alpha}L_{\operatorname{loc}}(\Omega)$. Moreover, each homeomorphism $f$ which introduces continuous composition operator from $WL^{q}\log^{\alpha}L$ to $WL^{q}\log^{\alpha}L$ is necessarily a $q$-quasiconformal mapping. As a new tool, we prove a Lebesgue density type theorem for Orlicz spaces.


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Stanislav Hencl. Luděk Kleprlík. "Composition of $q$-quasiconformal mappings and functions in Orlicz–Sobolev spaces." Illinois J. Math. 56 (3) 931 - 955, Fall 2012.


Published: Fall 2012
First available in Project Euclid: 31 January 2014

zbMATH: 1291.30133
MathSciNet: MR3161359
Digital Object Identifier: 10.1215/ijm/1391178556

Primary: 30C65 , 46E30 , 46E35

Rights: Copyright © 2012 University of Illinois at Urbana-Champaign

Vol.56 • No. 3 • Fall 2012
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