Displaying similar documents to “Variability sets on Riemann surfaces and forgetful maps between Teichmüller spaces.”

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.

On conformal dilatation in space.

Bishop, Christopher J., Gutlyanskiĭ, Vladimir Ya., Martio, Olli, Vuorinen, Matti (2003)

International Journal of Mathematics and Mathematical Sciences

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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.