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arXiv · 1604.08713

Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness

Josef Dick·Aicke Hinrichs·Lev Markhasin·Friedrich Pillichshammer
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Abstract

The discrepancy function measures the deviation of the empirical distribution of a point set in $[0,1]^d$ from the uniform distribution. In this paper, we study the classical discrepancy function with respect to the BMO and exponential Orlicz norms, as well as Sobolev, Besov and Triebel-Lizorkin norms with dominating mixed smoothness. We give sharp bounds for the discrepancy function under such norms with respect to infinite sequences.

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Josef Dick, Aicke Hinrichs, Lev Markhasin, Friedrich Pillichshammer. 2016-08-24. Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness. https://arxiv.org/abs/1604.08713

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