On convergence of Fourier series of Besicovitch almost periodic functions

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Abstract

The paper deals with convergence of the Fourier series of q-Besicovitch almost periodic functions of the form (Formula presented.) where {λm} is a Dirichlet sequence, that is, a strictly increasing sequence of nonnegative numbers tending to infinity. In particular, we show that, for 1 < q < ∞, the Fourier series of f(t) converges in norm to the function f(t) itself with usual order, which is analogous to the convergence in norm of the Fourier series of a function on [0, 2π]. A version of the Carleson-Hunt theorem is also investigated.

Original languageEnglish
Pages (from-to)264-279
Number of pages16
JournalLithuanian Mathematical Journal
Volume53
Issue number3
DOIs
Publication statusPublished - 2013 Jul

Keywords

  • Besicovitch almost periodic functions
  • Carleson-Hunt theorem
  • Fourier series
  • convergence in norm of Fourier series
  • martingale convergence theorem

ASJC Scopus subject areas

  • Mathematics(all)

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