On convergence of Fourier series of Besicovitch almost periodic functions

Trinh Khanh Duy

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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 - Jul 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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