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A Three Dimensional Signed Small Ball Inequality

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 نشر من قبل Michael T. Lacey
 تاريخ النشر 2009
  مجال البحث
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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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