Hardy-Sobolev Type Inequalities with Sharp Constants in Carnot-Carathéodory Spaces

Document Type

Article

Publication Date

4-1-2011

Abstract

We prove a generalization with sharp constants of a classical inequality due to Hardy to Carnot groups of arbitrary step, or more general Carnot-Carathéodory spaces associated with a system of vector fields of Hörmander type. Under a suitable additional assumption (see Eq. 1.6 below) we are able to extend such result to the nonlinear case p ne; 2. We also obtain a sharp inequality of Hardy-Sobolev type. © 2010 Springer Science+Business Media B.V.

Publication Source (Journal or Book title)

Potential Analysis

First Page

223

Last Page

242

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