Some functional inequalities for the fractional p-sub-Laplacian

Abstract

In this paper we study the fractional Dirichlet p-sub-Laplacian in a Haar measurable set on homogeneous Lie groups. We prove fractional Sobolev and Hardy inequalities and we also present a Lyapunov-type inequality for the fractional p-sub-Laplacian. As a consequence of the Lyapunov-type inequality we show an estimate of the first eigenvalue in a quasi-ball for the Dirichlet fractional p-sub-Laplacian.

a typo corrected version. 14 pages. submitted

References in corpus (3)

• Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups
• On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and $p$-sub-Laplacian inequalities on stratified groups
• Local Hardy and Rellich inequalities for sums of squares of vector fields