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

2016/04/29 by Josef Dick, Aicke Hinrichs, Dick, Josef +5
Mathematics · #11K06 #11K38 (Primary) #32A37 #42C10 #46E30 #46E35 #65C05 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11K06 #msc:11K38 #msc:32A37 #msc:42C10 #msc:46E30 #msc:46E35 #msc:65C05

paper · pdf · doi:10.48550/arxiv.1604.08713

A journal requested to split the first version of the paper arXiv:1601.07281 into two parts. This is the second part which contains the results on the BMO and exponential Orlicz norm of the discrepancy function. Further the discrepancy function in Sobolev-, Besov- and Triebel-Lizorkin spaces of dominating mixed smoothness is considered

arxiv created 2016/08/24 · arxiv updated 2016/08/25

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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