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

Donatella Danielli, Nicola Garofalo, Nguyen Cong Phuc

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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 languageEnglish (US)
Pages (from-to)223-242
Number of pages20
JournalPotential Analysis
Issue number3
StatePublished - Apr 2011
Externally publishedYes


  • Carnot groups
  • Carnot-Carathéodory spaces
  • Hardy type inequalities
  • Horizontal p-Laplacian

ASJC Scopus subject areas

  • Analysis


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