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

摘要

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