Remark on dimension-free estimates for discrete maximal functions over ℓ^q balls: small dyadic scales

2024/10/31 by Niksiński, Jakub
#42B15 #42B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.23993

Abstract

We give a dimension-free bound on ℓ^p(ℤ ^d), p ∈ [2, ∞] for the discrete Hardy-Littlewood maximal operator over the ℓ^q balls in ℤ ^d with small dyadic radii. Our result combined with the work of Kosz, Mirek, Plewa, Wróbel gives dimension-free estimates on ℓ^p(ℤ^d), p ∈ [2, ∞] for the discrete dyadic Hardy-Littlewood maximal operator over ℓ^q balls for q ≥ 2.

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