Hardy–Sobolev Type Inequalities with Sharp Constants in Carnot–Carathéodory Spaces
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- Danielli, D., Garofalo, N. & Phuc, N.C. Potential Anal (2011) 34: 223. doi:10.1007/s11118-010-9190-0
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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 \(p\not= 2\). We also obtain a sharp inequality of Hardy–Sobolev type.