TY - JOUR

T1 - On convergence of Fourier series of Besicovitch almost periodic functions

AU - Duy, Trinh Khanh

N1 - Funding Information:
1 The author is supported by JSPS Research Fellowships for Young Scientists.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 2013/7

Y1 - 2013/7

N2 - 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.

AB - 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.

KW - Besicovitch almost periodic functions

KW - Carleson-Hunt theorem

KW - Fourier series

KW - convergence in norm of Fourier series

KW - martingale convergence theorem

UR - http://www.scopus.com/inward/record.url?scp=84899418292&partnerID=8YFLogxK

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U2 - 10.1007/s10986-013-9207-7

DO - 10.1007/s10986-013-9207-7

M3 - Article

AN - SCOPUS:84899418292

SN - 0363-1672

VL - 53

SP - 264

EP - 279

JO - Lithuanian Mathematical Journal

JF - Lithuanian Mathematical Journal

IS - 3

ER -