David maps and Hausdorff dimension.
Zakeri, Saeed (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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Zakeri, Saeed (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.
Bishop, Christopher J., Tyson, Jeremy T. (2001)
Annales Academiae Scientiarum Fennicae. Mathematica
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Juha Heinonen (1996)
Revista Matemática Iberoamericana
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In this paper a quite complete picture is given of the absolute continuity on the boundary of a quasiconformal map B → D, where B is the unit 3-ball and D is a Jordan domain in R with boundary 2-rectifiable in the sense of geometric measure theory. Moreover, examples are constructed, for each n ≥ 3, showing that quasiconformal maps from the unit n-ball onto Jordan domains with boundary (n - 1)-rectifiable need not have absolutely continuous boundary values.
J. Zajac (1988)
Matematički Vesnik
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Michel Zinsmeister (1986)
Bulletin de la Société Mathématique de France
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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.
Rohde, S. (1997)
Annales Academiae Scientiarum Fennicae. Mathematica
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Tyutyuev, A.V., Shlyk, V.A. (2004)
Zapiski Nauchnykh Seminarov POMI
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V. P. Mićić (1972)
Matematički Vesnik
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Kovalev, Leonid V. (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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Xinzhong Huang (2014)
Annales Polonici Mathematici
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We give a Hölder type estimate for normalized ρ-quasisymmetric functions, improving some results of J. Zając.