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On the Small Ball Inequality in all dimensions |
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| Authors: | Dmitriy Bilyk Armen Vagharshakyan |
| Institution: | School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30030, USA |
| Abstract: | Let hR denote an L∞ normalized Haar function adapted to a dyadic rectangle R⊂d0,1]. We show that for choices of coefficients α(R), we have the following lower bound on the L∞ norms of the sums of such functions, where the sum is over rectangles of a fixed volume: |
| Keywords: | Discrepancy function Small ball inequality Brownian Sheet Haar functions Littlewood-Paley Inequalities Kolmogorov entropy Mixed derivative |
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