Norms of spherical averaging operators for some geometric group actions

2024/05/14 by Bogdan Nica, Nica, Bogdan · 1 citation
Mathematics · Medicine · Physics and Astronomy · #20F67 #43A15 #Advanced Algebra and Geometry #Advanced Differential Geometry Research #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Medical Imaging Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2405.08682

openalex publication_date 2024/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain asymptotic estimates for the ℓ^p-operator norm of spherical averaging operators associated to certain geometric group actions. The motivating example is the case of Gromov hyperbolic groups, for which we obtain asymptotically sharp estimates. We deduce asymptotic lower bounds for the combinatorial expansion of spheres.

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