Sobolev homeomorphisms and composition operators

Vladimir Gol’dshtein, Alexander Ukhlov

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


We study the invertibility of bounded composition operators of Sobolev spaces. We prove that if a homeomorphism ϕ of Euclidean domains D and D0 generates, by the composition rule ϕ∗f = f◦ϕ, a bounded composition operator of the Sobolev spaces ϕ∗ : L1∞(D0) → L1 p(D), p > n − 1, has finite distortion and the Luzin N-property, then the inverse ϕ−1 generates thebounded composition operator from L1 p0 (D), p0 = p/(p − n + 1), into L11(D0)
Original languageEnglish
Title of host publicationAround the Research of Vladimir Maz'ya I
Number of pages14
ISBN (Electronic)978-1-4419-1341-8
ISBN (Print)978-1-4419-1340-1
StatePublished - 2010


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