Displaying similar documents to “Some remarks concerning quasiconformal extensions in several complex variables.”

An inverse Sobolev lemma.

Pekka Koskela (1994)

Revista Matemática Iberoamericana


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.

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

Luděk Kleprlík (2014)

Open Mathematics


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.