Abstract
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 language | English |
|---|---|
| Title of host publication | Around the Research of Vladimir Maz'ya I |
| Publisher | Springer |
| Pages | 207-220 |
| Number of pages | 14 |
| ISBN (Electronic) | 978-1-4419-1341-8 |
| ISBN (Print) | 978-1-4419-1340-1 |
| DOIs | |
| State | Published - 2010 |