IMPROVED HARDY-SOBOLEV INEQUALITIES

Abstract

In this thesis work, a new version of the Hardy-Sobolev inequality is obtained. It covers the recent inequality of Frank, Laptev, and Weidl derived in [4] and improves the results of Persson and Samko established in [13]. It gives new results in one dimension. We analyse radial and non-radial versions of the considered multidimensional Hardy-Sobolev inequality and as a consequence we establish some Heisenberg-Pauli-Weyl uncertainty principles.