Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness
Abstract
The discrepancy function measures the deviation of the empirical distribution of a point set in 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.
Cite
@article{arxiv.1604.08713,
title = {Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness},
author = {Josef Dick and Aicke Hinrichs and Lev Markhasin and Friedrich Pillichshammer},
journal= {arXiv preprint arXiv:1604.08713},
year = {2016}
}
Comments
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