Hardy spaces and convergence of vector-valued Vilenkin-Fourier series

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The atomic decomposition of a vector-valued martingale Hardy space is given. A classical inequality of Marcinkiewicz is generalized for UMD lattice valued (bounded) Vilenkin-Fourier series. It is proved that the Vilenkin-Fourier series of f ∈ L P(X) (1 < p < ∞) converges to f in L p(X) norm if and only if X is a UMD space. Moreover, a lacunary sequence of the UMD lattice valued Vilenkin-Fourier series of f ∈ H 1 (X) converges almost everywhere to f in X norm.

Original languageEnglish
Pages (from-to)413-424
Number of pages12
JournalPublicationes Mathematicae
Issue number3-4
Publication statusPublished - Nov 22 2007


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

ASJC Scopus subject areas

  • Mathematics(all)

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