English

Abstract

Hardy and Rellich type inequalities with an additional term are proved for compactly supported smooth functions on open subsets of the Euclidean space. We obtain one-dimensional Hardy type inequalities and their multidimensional analogues in convex domains with the finite inradius. We use Bessel functions and the Lamb constant. The statements proved are a generalization for the case of arbitrary p ⩾ 2 of the corresponding inequality proved by F. G. Avkhadiev, K.-J. Wirths (2011) for p = 2. Also we establish Rellich type inequalities on arbitrary domains, regular sets, on domains with θ-cone condition and on convex domains.