Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings
Let \(D\) and \(D'\) be domains in a Carnot group \(G\) whose Hausdorff dimension is \(\nu\), \(L_p^1(D)\) be the homogeneous Sobolev space on \(D\), \(p\geq 1\), \(p\neq\nu\). In the paper under review, the authors study the properties of a measurable mapping \(\varphi: D\mapsto D'\) for which the superposition operator \(\varphi^*: f\mapsto f\circ\varphi\) is an isomorphism of the homogeneous Sobolev spaces \(L_p^1(D)\) and \(L_p^1(D')\).
scientific article; zbMATH DE number 6386964
scientific article