Dimension-free L2 maximal inequality for spherical means in the hypercube

Aram W. Harrow, Alexandra Kolla, Leonard J. Schulman

Research output: Contribution to journalArticlepeer-review

Abstract

We establish the maximal inequality claimed in the title. In combinatorial terms this has the implication that for sufficiently small ε > 0, for all n, any marking of an e 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.

Original languageEnglish (US)
Pages (from-to)55-75
Number of pages21
JournalTheory of Computing
Volume10
DOIs
StatePublished - May 23 2014

Keywords

  • Boolean hypercube
  • Fourier analysis
  • Maximal inequality

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

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