A characterization of the uniform strong type (1,1) bounds for averaging operators

2019/02/28 by J. M. Aldaz, Aldaz, J. M.
Mathematics · #41A35 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fixed Point Theorems Analysis #math.CA #msc:41A35

paper · pdf · doi:10.48550/arxiv.1902.11080

arXiv admin note: text overlap with arXiv:1811.10478

arxiv created 2019/02/28 · openalex publication_date 2019/02/28 · arxiv updated 2019/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that in a metric measure space (X, d, μ), the averaging operators A_{r, μ} satisfy a uniform strong type (1,1) bound sup_{r, μ} ‖A_{r, μ}‖_{L¹→ L¹} < ∞ if and only if X satisfies a certain geometric condition, the equal radius Besicovitch intersection property.

Citations

• Kissing numbers and the centered maximal operator

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• Kissing numbers and the centered maximal operator

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