Sobolev spaces and \((P,Q)\)-quasiconformal mappings of Carnot groups
Measurable functions \(\varphi \: G\to G'\) are considered which induce an isomorphism \(\varphi^*\) between the Sobolev spaces \(L^1_n(G)\) and \(L^1_n(G')\) by the rule \(\varphi^*(f)=f\circ \varphi\), \(f\in L^1_n\). Here \(G\subset \mathbb R^n\), \(G'\subset \mathbb R^n\), and the Sobolev spaces \(L^1_n(G)\), \(L^1_n(G')\) are equipped with the Carnot--Carathéodory metric. Metric and analytic properties are also studied of mappings which induce bounded embedding operators \(\varphi^* \:L^1_p(G) \to L^1_q(G')\), \(1\leq q\leq p<\infty\).
scientific article; zbMATH DE number 1285466