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Harnack inequality for fractional sub-Laplacians in Carnot groups

2014; Springer Science+Business Media; Volume: 279; Issue: 1-2 Linguagem: Inglês

10.1007/s00209-014-1376-5

1432-1823

Fausto Ferrari, Bruno Franchi,

Geometric Analysis and Curvature Flows

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.