Wiener amalgams, Hardy spaces and summability of Fourier series

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Abstract

A general summability method, the so called θ-summability is considered for multi-dimensional Fourier series, where θ is in the Wiener algebra W(C,ℓ1)(ℝd). It is based on the use of Wiener amalgam spaces, weighted Feichtinger's algebra, Herz and Hardy spaces. Under some conditions on θ, it is proved that the maximal operator of the θ-means is bounded from the Hp Hardy space to Lp (or Hp). This implies some norm and almost everywhere convergence results for the θ-means. Large number of special cases of the θ-summation are considered.

Original languageEnglish
Pages (from-to)419-442
Number of pages24
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume145
Issue number2
DOIs
Publication statusPublished - Sep 1 2008

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ASJC Scopus subject areas

  • Mathematics(all)

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