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Some functional inequalities for the fractional p-sub-Laplacian

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arxiv 1804.01415 v2 pith:6LYGTLJ6 submitted 2018-04-04 math.AP

Some functional inequalities for the fractional p-sub-Laplacian

Aidyn Kassymov , Durvudkhan Suragan This is my paper
classification math.AP
keywords fractionalp-sub-laplaciandirichletinequalitiesinequalitylyapunov-typeconsequenceeigenvalue
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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.

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