Sobolev-Type Inequalities for Dunkl Operators

2018/11/27 by Andrei Velicu, Velicu, Andrei · 2 citations
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1811.11118

openalex publication_date 2018/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the Sobolev inequality in the Dunkl setting using two new approaches which provide a simpler elementary proof of the classical case p=2, as well as an extension to the coefficient p=1 that was previously unknown. We also find estimates of the sharp constants for the Sobolev inequality for Dunkl gradient. Related inequalities and some improvements are also considered (Nash inequality, Besov space embeddings).

Cited by

• Bessel and Dunkl processes with drift
• Caccioppoli-type inequalities for the Dunkl-A-Laplacian and their application to nonexistence result

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