Characterizations of snowflake metric spaces.
Composition operator and Sobolev-Lorentz spaces
Let Ω,Ω’ ⊂ ℝⁿ be domains and let f: Ω → Ω’ be a homeomorphism. We show that if the composition operator maps the Sobolev-Lorentz space to for some q ≠ n then f must be a locally bilipschitz mapping.
Composition operators on W 1 X are necessarily induced by quasiconformal mappings
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.
Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary.
Continua of bounded turning: chain condition and infinitesimal connectedness.
Continuously removable sets for quasiconformal mappings.
Correction to the article `Deformation of plates of small condensers and Belinskij's problem'.
Cyclic parabolic quasiconformal groups that are not quasiconformal conjugates of Möbius groups.