Dimension-free Maximal Inequalities for Spherical Means in the Hypercube

2013/09/17 by Ben Krause, Krause, Ben · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Mathematical Approximation and Integration #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1309.4466

openalex publication_date 2013/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the main result of Harrow, Kolla, and Schulman -- the existence of dimension-free L²-bounds for the spherical maximal function in the hypercube -- to all L^p, p > 1. Our approach is motivated by the spectral technique developed by Stein and Nevo and Stein in the context of pointwise ergodic theorems on general groups. We provide an example which demonstrates that no dimension-free weak-type (1-1) bound exists at the endpoint.

Citations

• On the Hardy-Littlewood maximal function for the cube

Cited by

• Dimension-Free Estimates for Noncommutative Discrete Maximal Spherical Means

Related

• Spherical maximal estimates via geometry
• Dimension-free estimates for the discrete spherical maximal functions
• A note on generalized spherical maximal means
• On the maximal function associated to the spherical means on the Heisenberg group
• On the lacunary spherical maximal function on the Heisenberg group