Functional inequalities for a class of nonlocal hypoelliptic equations of H\"ormander type
Abstract
We consider a class of second-order partial differential operators of H\"ormander type, which contain as a prototypical example a well-studied operator introduced by Kolmogorov in the '30s. We analyze some properties of the nonlocal operators driven by the fractional powers of , and we introduce some interpolation spaces related to them. We also establish sharp pointwise estimates of Harnack type for the semigroup associated with the extension operator. Moreover, we prove both global and localised versions of Poincar\'e inequalities adapted to the underlying geometry.
Keywords
Cite
@article{arxiv.1905.08887,
title = {Functional inequalities for a class of nonlocal hypoelliptic equations of H\"ormander type},
author = {Nicola Garofalo and Giulio Tralli},
journal= {arXiv preprint arXiv:1905.08887},
year = {2019}
}
Comments
The paper is going to appear in Nonlinear Anal., Special Issue on "Fractional and Nonlocal equations". The content of Section 5 had been originally announced in a first preliminary version of the ArXiv preprint 1811.02968