Some global Sobolev inequalities related to Kolmogorov-type operators

Giulio Tralli

Abstract


In this note we review a recent result in [17] in collaboration with N. Garofalo, where we establish global versions of Hardy-Littlewood-Sobolev inequalities attached to hypoelliptic equations of Kolmogorov type. The relevant Sobolev spaces are defined through the fractional powers of the operator under consideration. We outline the main steps of the semigroup approach we adopt.


Keywords


Global a priori estimates; Kolmogorov-Fokker-Planck diffusion; fractional powers of hypoelliptic operators

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References


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DOI: 10.6092/issn.2240-2829/10584

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