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Weak Type Estimates for the Noncommutative Vilenkin–Fourier Series

  • Thomas Tzvi Scheckter
  • Fedor Sukochev
Article
  • 43 Downloads

Abstract

Let \({\mathcal {R}}\) be the separable hyperfinite factor of type \(\text {II}_1\). We show that for any bounded Vilenkin group, the sequence of partial sums of the corresponding noncommutative Vilenkin–Fourier series is a uniformly bounded family of weak type (1, 1) operators.

Keywords

Noncommutative martingales Vilenkin groups Vilenkin–Fourier series 

Mathematics Subject Classification

Primary 46L52 Secondary 46L53 47A30 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of New South WalesKensingtonAustralia

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