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  • Josef Dick (a1), Aicke Hinrichs (a2), Lev Markhasin (a3) and Friedrich Pillichshammer (a4)

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 bounded mean oscillation 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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  • ISSN: 0025-5793
  • EISSN: 2041-7942
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