Restricted summability of Fourier transforms and local Hardy spaces

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Abstract

A general summability method, the so-called Θ-summability is considered for multi-dimensional Fourier transforms. Under some conditions on Θ, it is proved that the maximal operator of the Θ-means defined in a cone is bounded from the amalgam Hardy space W(hp, ℓ) to W(Lp, ℓ). This implies the almost everywhere convergence of the Θ-means in a cone for all f ∈ W(L1, ℓ) ⊃ L1.

Original languageEnglish
Pages (from-to)1627-1640
Number of pages14
JournalActa Mathematica Sinica, English Series
Volume26
Issue number9
DOIs
Publication statusPublished - Aug 20 2010

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Keywords

  • Wiener amalgam spaces
  • atomic decomposition
  • local Hardy spaces
  • Θ-summability of Fourier transforms

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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