Almost everywhere convergence of Banach space-valued Vilenkin-Fourier series

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3 Citations (Scopus)

Abstract

The duality between martingale Hardy and BMO spaces is generalized for Banach space valued martingales. It is proved that if X is a UMD Banach space and f L p(X) for some 1 < p < ∞ then the Vilenkin-Fourier series of f converges to f almost everywhere in X norm, which is the extension of Carleson's result.

Original languageEnglish
Pages (from-to)47-59
Number of pages13
JournalActa Mathematica Hungarica
Volume116
Issue number1-2
DOIs
Publication statusPublished - Jul 1 2007

Keywords

  • Atomic decomposition
  • UMD spaces
  • Vector-valued Hardy and BMO spaces
  • Vector-valued Vilenkin-Fourier series

ASJC Scopus subject areas

  • Mathematics(all)

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