Hardy and Rellich-type inequalities for metrics defined by vector fields
The author considers a system of locally Lipschitz fields on a domain in \(\mathbb{R}^n\). It is assumed that the Lebesgue measure is doubling and a scaled \(L^1\)-Poincaré inequality holds. Non-local analogues of both Hardy and Sobolev-Okikiolu inequalities are obtained. Some applications are considered.
scientific article; zbMATH DE number 1901239