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arXiv · 1206.0885

Harnack inequality for fractional sub-Laplacians in Carnot groups

Fausto Ferrari·Bruno Franchi
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Abstract

In this paper we prove an invariant Harnack inequality on Carnot-Carathéodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a technique recently introduced by Caffarelli and Silvestre. In addition, we write explicitly the Poisson kernel for a class of degenerate subelliptic equations in product-type Carnot groups.

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Fausto Ferrari, Bruno Franchi. 2013-02-04. Harnack inequality for fractional sub-Laplacians in Carnot groups. https://doi.org/10.1007/s00209-014-1376-5

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