Dimension-Free $L^p$-Maximal Inequalities for Spherical Means in the Hypercube

Ben Krause

Type: Article

Publication Date: 2018-01-01

Citations: 0

DOI: https://doi.org/10.1137/140961663

Abstract

We extend the main result of Harrow, Kolla, and Schulman---the existence of dimension-free $L^2$-bounds for the spherical maximal function in the hypercube, $\{0,1\}^N$---to all $L^p, p > 1$. Our approach is motivated by the spectral technique developed by Nevo and Stein, and by 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.

Locations

SIAM Journal on Discrete Mathematics - View
arXiv (Cornell University) - PDF

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