Inequalities of Hardy-Sobolev type in Carnot-Carathéodory spaces - Mathematics > Analysis of PDEsReport as inadecuate




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Abstract: We consider various types of Hardy-Sobolev inequalities on aCarnot-Carath\-eodory space $\Om, d$ associated to a system of smooth vectorfields $X=\{X 1, X 2,

.,X m\}$ on $\RR^n$ satisfying the H\-ormander-s finiterank condition $rank LieX 1,

.,X m \equiv n$. One of our main concerns isthe trace inequality\int {\Om}|\phix|^{p}Vxdx\leq C\int {\Om}|X\phi|^{p}dx,\qquad \phi\inC^{\infty} {0}\Om,where $V$ is a general weight, i.e., a nonnegative locally integrablefunction on $\Om$, and $1


Author: Donatella Danielli, Nicola Garofalo, Nguyen Cong Phuc

Source: https://arxiv.org/







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