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.
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.
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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 -