On convergence of Fourier series of Besicovitch almost periodic functions

Khanh Duy Trinh

Research output: Contribution to journalArticle

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 Jan 1
Externally publishedYes

Fingerprint

Almost Periodic Functions
Fourier series
Norm
Monotonic increasing sequence
Dirichlet
Strictly
Non-negative
Infinity
Converge
Theorem

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On convergence of Fourier series of Besicovitch almost periodic functions. / Trinh, Khanh Duy.

In: Lithuanian Mathematical Journal, Vol. 53, No. 3, 01.01.2013, p. 264-279.

Research output: Contribution to journalArticle

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