Relative Nash-type and \(L^2\)-Sobolev inequalities for Dunkl operators and applications

We investigate local variants of Nash inequalities in the context of Dunkl operators. Pseudo-Poincaré inequalities are first established using pointwise gradient estimates of the Dunkl heat kernel. These inequalities allow to obtain relative Nash-type inequalities which are used to derive mean value...

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Bibliographic Details
Published in:arXiv.org 2021-02
Main Authors: Mustapha, S, Sifi, M
Format: Article
Language:English
Subjects:
Inequalities
Operators
Thermodynamics
Online Access:Get full text
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Summary:We investigate local variants of Nash inequalities in the context of Dunkl operators. Pseudo-Poincaré inequalities are first established using pointwise gradient estimates of the Dunkl heat kernel. These inequalities allow to obtain relative Nash-type inequalities which are used to derive mean value inequalities for subsolutions of the heat equation on orbits of balls not necessarily centered on the origin.
ISSN:2331-8422