Pointwise convergence in Pringsheim’s sense of the summability of Fourier transforms on Wiener amalgam spaces

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Abstract

New multi-dimensional Wiener amalgam spaces (Formula presented.)(Rd) are introduced by taking the usual one-dimensional spaces coordinatewise in each dimension. The strong Hardy-Littlewood maximal function is investigated on these spaces. The pointwise convergence in Pringsheim’s sense of the θ-summability of multi-dimensional Fourier transforms is studied. It is proved that if the Fourier transform of θ is in a suitable Herz space, then the θ-means (Formula presented.) converge to f a.e. for all (Formula presented.)(Rd). Note that (Formula presented.) and (Formula presented.), where 1<r≤∞. Moreover, (Formula presented.) converges to f(x) at each Lebesgue point of (Formula presented.).

Original languageEnglish
Pages (from-to)143-160
Number of pages18
JournalMonatshefte fur Mathematik
Volume175
Issue number1
DOIs
Publication statusPublished - Sep 1 2014

Keywords

  • Herz spaces
  • Lebesgue points
  • Strong Hardy-Littlewood maximal function
  • Wiener amalgam spaces
  • θ-summability

ASJC Scopus subject areas

  • Mathematics(all)

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