Harnack inequality for fractional sub-Laplacians in Carnot groups. (English) Zbl 1314.26008
An invariant Harnack inequality on Carnot-Carathéodory balls for fractional powers of sub-Laplacians in Carnot groups is derived and proved using the abstract formulation technique introduced by L. Caffarelli and L. Silvestre [Commun. Partial Differ. Equations 32, No. 8, 1245–1260 (2007; Zbl 1143.26002)]. Furthermore, an explicit Poisson kernel for a class of degenerate sub-elliptic equations in product-type Carnot groups are similarly derived and proved.
Reviewer: James Adedayo Oguntuase (Abeokuta)
MSC:
| 26A33 | Fractional derivatives and integrals |
| 35R03 | PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. |
Citations:
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