Dimension-free L2 maximal inequality for spherical means in the hypercube
Combinatorics
2014-05-30 v2 Classical Analysis and ODEs
Abstract
We establish the result of the title. In combinatorial terms this has the implication that for sufficiently small eps > 0, for all n, any marking of an eps fraction of the vertices of the n-dimensional hypercube necessarily leaves a vertex x such that marked vertices are a minority of every sphere centered at x.
Cite
@article{arxiv.1209.4148,
title = {Dimension-free L2 maximal inequality for spherical means in the hypercube},
author = {Aram W. Harrow and Alexandra Kolla and Leonard J. Schulman},
journal= {arXiv preprint arXiv:1209.4148},
year = {2014}
}
Comments
17 pages. v2. This version matches the published version and fixes typos, simplifies some proofs and makes other minor changes. The main results are unchanged from v1