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• W2952993543 abstract "We study the local discrepancy of a symmetrized version of the well-known van der Corput sequence and of modified two-dimensional Hammersley point sets in arbitrary base $b$. We give upper bounds on the norm of the local discrepancy in Besov spaces of dominating mixed smoothness $S_{pq}^rB([0,1)^s)$, which will also give us bounds on the $L_p$-discrepancy. Our sequence and point sets will achieve the known optimal order for the $L_p$- and $S_{pq}^rB$-discrepancy. The results in this paper generalize several previous results on $L_p$- and $S_{pq}^rB$-discrepancy estimates and provide a sharp upper bound on the $S_{pq}^rB$-discrepancy of one-dimensional sequences for $r>0$. We will use the $b$-adic Haar function system in the proofs." @default.
• W2952993543 created "2019-06-27" @default.
• W2952993543 creator A5056005645 @default.
• W2952993543 date "2015-07-07" @default.
• W2952993543 modified "2023-09-27" @default.
• W2952993543 title "L_p- and S_{p,q}^rB-discrepancy of the symmetrized van der Corput sequence and modified Hammersley point sets in arbitrary bases" @default.
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• W2952993543 hasPublicationYear "2015" @default.
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