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.
Original language | English (US) |
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Pages (from-to) | 223-242 |
Number of pages | 20 |
Journal | Potential Analysis |
Volume | 34 |
Issue number | 3 |
DOIs | |
State | Published - Apr 2011 |
Externally published | Yes |
Keywords
- Carnot groups
- Carnot-Carathéodory spaces
- Hardy type inequalities
- Horizontal p-Laplacian
ASJC Scopus subject areas
- Analysis