Pointwise summability of Gabor expansions

Research output: Article

3 Citations (Scopus)

Abstract

A general summability method, the so-called θ-summability method is considered for Gabor series. It is proved that if the Fourier transform of θ is in a Herz space then this summation method for the Gabor expansion of f converges to f almost everywhere when f∈L1 or, more generally, when f∈W(L1,ℓ) (Wiener amalgam space). Some weak type inequalities for the maximal operator corresponding to the θ-means of the Gabor expansion are obtained. Hardy-Littlewood type maximal functions are introduced and some inequalities are proved for these.

Original languageEnglish
Pages (from-to)463-487
Number of pages25
JournalJournal of Fourier Analysis and Applications
Volume15
Issue number4
DOIs
Publication statusPublished - okt. 1 2009

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Applied Mathematics

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