NDLI: L p -discrepancy of the symmetrized van der Corput sequence

Content Provider	Springer Nature Link
Author	Kritzinger, Ralph Pillichshammer, Friedrich
Copyright Year	2015
Abstract	It is well known that the L p -discrepancy for $${p \in [1,\infty]}$$ of the van der Corput sequence is of exact order of magnitude $${O((\log N)/N)}$$ . This however is for $${p \in (1,\infty)}$$ not best possible with respect to the lower bounds according to Roth and Proinov. For the case $${p=2}$$ , it is well known that the symmetrization trick due to Davenport leads to the optimal L 2-discrepancy rate $${O(\sqrt{\log N}/N)}$$ for the symmetrized van der Corput sequence. In this note we show that this result holds for all $${p \in [1,\infty)}$$ . The proof is based on an estimate of the Haar coefficients of the corresponding local discrepancy and on the use of the Littlewood-Paley inequality.
Ending Page	418
Page Count	12
Starting Page	407
File Format	PDF
ISSN	0003889X
e-ISSN	14208938
Journal	Archiv der Mathematik
Issue Number	5
Volume Number	104
Language	English
Publisher	Springer Basel
Publisher Date	2015-04-18
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Irregularities of distribution, discrepancy Special sequences Van der Corput sequence Davenport’s reflection principle Mathematics L p -discrepancy
Content Type	Text
Resource Type	Article
Subject	Mathematics

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L p -discrepancy of the symmetrized van der Corput sequence