A Three Dimensional Signed Small Ball Inequality

Details A Three Dimensional Signed Small Ball Inequality A Three Dimensional Signed Small Ball Inequality

2009-09-28

arxiv.org/abs/0909.5158v2

Mathematics

Classical Analysis and ODEs

13 pages. To appear in Walter Philipp memorial volume. v2 incorporates the referee's report

Scientific paper

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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