### 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 language | English |
---|---|

Pages (from-to) | 264-279 |

Number of pages | 16 |

Journal | Lithuanian Mathematical Journal |

Volume | 53 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2013 Jan 1 |

Externally published | Yes |

### Fingerprint

### 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

*Lithuanian Mathematical Journal*,

*53*(3), 264-279. https://doi.org/10.1007/s10986-013-9207-7

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

Research output: Contribution to journal › Article

*Lithuanian Mathematical Journal*, vol. 53, no. 3, pp. 264-279. https://doi.org/10.1007/s10986-013-9207-7

}

TY - JOUR

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

AU - Trinh, Khanh Duy

PY - 2013/1/1

Y1 - 2013/1/1

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 - convergence in norm of Fourier series

KW - Fourier series

KW - martingale convergence theorem

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

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

U2 - 10.1007/s10986-013-9207-7

DO - 10.1007/s10986-013-9207-7

M3 - Article

AN - SCOPUS:84899418292

VL - 53

SP - 264

EP - 279

JO - Lithuanian Mathematical Journal

JF - Lithuanian Mathematical Journal

SN - 0363-1672

IS - 3

ER -