Quasiregular mappings of maximal local modulus of continuity.
Kovalev, Leonid V. (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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Kovalev, Leonid V. (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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Michel Zinsmeister (1986)
Bulletin de la Société Mathématique de France
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Matti Vuorinen (1983)
Banach Center Publications
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Mayer, Volker (2000)
Annales Academiae Scientiarum Fennicae. Mathematica
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Rajala, Kai (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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Luděk Kleprlík (2014)
Open Mathematics
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Let Ω ⊂ ℝn be an open set and X(Ω) be any rearrangement invariant function space close to L q(Ω), i.e. X has the q-scaling property. We prove that each homeomorphism f which induces the composition operator u ↦ u ℴ f from W 1 X to W 1 X is necessarily a q-quasiconformal mapping. We also give some new results for the sufficiency of this condition for the composition operator.
Bonfert-Taylor, Petra, Bridgeman, Martin, Taylor, Edward C. (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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Earle, Clifford J., Lakic, Nikola (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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Gutlyanskij, V.Ya., Martio, O., Ryazanov, V.I., Vuorinen, M. (2000)
Annales Academiae Scientiarum Fennicae. Mathematica
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Pekka Koskela (1994)
Revista Matemática Iberoamericana
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We establish an inverse Sobolev lemma for quasiconformal mappings and extend a weaker version of the Sobolev lemma for quasiconformal mappings of the unit ball of R to the full range 0 < p < n. As an application we obtain sharp integrability theorems for the derivative of a quasiconformal mapping of the unit ball of R in terms of the growth of the mapping.