Relative Nash-type and \(L^2\)-Sobolev inequalities in Dunkl setting

DOI10.1007/s11785-021-01164-wzbMath1478.35010arXiv2009.03405OpenAlexW3205994251MaRDI QIDQ2054432

Sami Mustapha, Mohamed Sifi

Publication date: 2 December 2021

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.03405

zbMATH Keywords

Sobolev inequalityNash inequalityDunkl operatorspseudo-Poincaré inequality

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Inequalities involving derivatives and differential and integral operators (26D10) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Heat kernel (35K08)

Related Items

Logarithmic Sobolev inequalities for Dunkl operators with applications to functional inequalities for singular Boltzmann-Gibbs measures

Cites Work

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• Harmonic functions, conjugate harmonic functions and the Hardy space \(H^1\) in the rational Dunkl setting
• Continuity of Solutions of Parabolic and Elliptic Equations
• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance
• An Introduction to Dunkl Theory and Its Analytic Aspects
• Sobolev inequalities in disguise
• A harnack inequality for parabolic differential equations

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