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arXiv · 0909.5158

A Three Dimensional Signed Small Ball Inequality

Dmitriy Bilyk·Michael T. Lacey·Ioannis Parissis·Armen Vagharshakyan
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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.

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Dmitriy Bilyk, Michael T. Lacey, Ioannis Parissis, Armen Vagharshakyan. 2009-09-28. A Three Dimensional Signed Small Ball Inequality. https://arxiv.org/abs/0909.5158

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