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

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
Volume71
Issue number3-4
Publication statusPublished - Nov 22 2007

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Hardy spaces and convergence of vector-valued Vilenkin-Fourier series'. Together they form a unique fingerprint.

  • Cite this