$L_p$- and $S_{p,q}^{r}B$-discrepancy of (order 2) digital nets

@article{LevMarkhasin2015,
abstract = {Dick proved that all dyadic order 2 digital nets satisfy optimal upper bounds on the $L_p$-discrepancy. We prove this for arbitrary prime base b with an alternative technique using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds on the discrepancy function in Besov spaces with dominating mixed smoothness for a certain parameter range, and enlarge that range for order 2 digital nets. The discrepancy function in Triebel-Lizorkin and Sobolev spaces with dominating mixed smoothness is considered as well.},
author = {Lev Markhasin},
journal = {Acta Arithmetica},
keywords = {-discrepancy; order 2 digital nets; dominating mixed smoothness; quasi-Monte Carlo; Haar system; Walsh system},
language = {eng},
number = {2},
pages = {139-159},
title = {$L_p$- and $S_\{p,q\}^rB$-discrepancy of (order 2) digital nets},
url = {http://eudml.org/doc/279520},
volume = {168},
year = {2015},
}

TY - JOUR
AU - Lev Markhasin
TI - $L_p$- and $S_{p,q}^rB$-discrepancy of (order 2) digital nets
JO - Acta Arithmetica
PY - 2015
VL - 168
IS - 2
SP - 139
EP - 159
AB - Dick proved that all dyadic order 2 digital nets satisfy optimal upper bounds on the $L_p$-discrepancy. We prove this for arbitrary prime base b with an alternative technique using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds on the discrepancy function in Besov spaces with dominating mixed smoothness for a certain parameter range, and enlarge that range for order 2 digital nets. The discrepancy function in Triebel-Lizorkin and Sobolev spaces with dominating mixed smoothness is considered as well.
LA - eng
KW - -discrepancy; order 2 digital nets; dominating mixed smoothness; quasi-Monte Carlo; Haar system; Walsh system
UR - http://eudml.org/doc/279520
ER -