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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The authors are supported by MURST, Italy, and by University of Bologna, Italy, funds for selected research topics and by EC Project CG-DICE.
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Ferrari, F., Franchi, B. Harnack inequality for fractional sub-Laplacians in Carnot groups. Math. Z. 279, 435–458 (2015). https://doi.org/10.1007/s00209-014-1376-5
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DOI: https://doi.org/10.1007/s00209-014-1376-5