A Three Dimensional Signed Small Ball Inequality
Classical Analysis and ODEs
2012-05-04 v2 Probability
Abstract
The Small Ball Inequality is a conjectural lower bound on sums the L-infinity norm of sums of Haar functions supported on dyadic rectangles of a fixed volume in the unit cube. The conjecture is fundamental to questions in discrepancy theory, approximation theory and probability theory. In this article, we concentrate on a special case of the conjecture, and give the best known lower bound in dimension 3, using a conditional expectation argument.
Keywords
Cite
@article{arxiv.0909.5158,
title = {A Three Dimensional Signed Small Ball Inequality},
author = {Dmitriy Bilyk and Michael T. Lacey and Ioannis Parissis and Armen Vagharshakyan},
journal= {arXiv preprint arXiv:0909.5158},
year = {2012}
}
Comments
13 pages. To appear in Walter Philipp memorial volume. v2 incorporates the referee's report