Displaying similar documents to “Distortion of the exponent of convergence in space.”

Composition operators on W 1 X are necessarily induced by quasiconformal mappings

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.

An inverse Sobolev lemma.

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.

Smooth quasiregular maps with branching in 𝐑 n

Robert Kaufman, Jeremy T. Tyson, Jang-Mei Wu (2005)

Publications Mathématiques de l'IHÉS

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According to a theorem of Martio, Rickman and Väisälä, all nonconstant C-smooth quasiregular maps in , ≥3, are local homeomorphisms. Bonk and Heinonen proved that the order of smoothness is sharp in . We prove that the order of smoothness is sharp in . For each ≥5 we construct a C-smooth quasiregular map in with nonempty branch set.