Sobolev embedding properties on compact matrix quantum groups of Kac\n type

2018/11/26 by Sang-Gyun Youn, Youn, Sang-Gyun
Mathematics · Physics and Astronomy · #20G42 #43A15 #46L52 #81R15 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.1811.10511

openalex publication_date 2018/11/26 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28

Abstract

We establish sharp Sobolev embedding properties within a broad class of\ncompact matrix quantum groups of Kac type under the polynomial growth or the\nrapid decay property of their duals. Main examples are duals of polynomially\ngrowing discrete quantum groups, duals of free groups and free quantum groups\nO_N⁺,S_N⁺. In addition, we generalize sharpend Hausdorff-Young\ninequalities, compute degrees of the rapid decay property for\n widehatO_N⁺, widehatS_N⁺ and prove sharpness of Hardy-Littlewood\ninequalities on duals of free groups.\n

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