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Harnack inequality for fractional sub-Laplacians in Carnot groups

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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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Authors and Affiliations

  1. Dipartimento di Matematica, Piazza di Porta S. Donato 5, 40126, Bologna, Italy

    Fausto Ferrari & Bruno Franchi

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  1. Fausto Ferrari
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  2. Bruno Franchi
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Correspondence to Fausto Ferrari.

Additional information

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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