### Abstract

Sufficient conditions are given for the convergence of the series ∑_{n=1}^{∞} λ(n)φ(|C_{n}|), where C_{n} are the Haar-Fourier coefficients of an integrable function, φ(x) (x ≥ 0, φ(0) = 0) is an increasing and concave function, and λ(x) (x ≥ 1) denotes a function satisfying certain easily achievable conditions.

Original language | English |
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Pages (from-to) | 263-269 |

Number of pages | 7 |

Journal | Mathematical Inequalities and Applications |

Volume | 5 |

Issue number | 2 |

Publication status | Published - Apr 2002 |

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### Keywords

- Absolute convergence
- Convave function
- Haar-system
- Power-monotone sequences

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematical Inequalities and Applications*,

*5*(2), 263-269.

**On the series of Haar-Fourier coefficients.** / Leindler, L.

Research output: Contribution to journal › Article

*Mathematical Inequalities and Applications*, vol. 5, no. 2, pp. 263-269.

}

TY - JOUR

T1 - On the series of Haar-Fourier coefficients

AU - Leindler, L.

PY - 2002/4

Y1 - 2002/4

N2 - Sufficient conditions are given for the convergence of the series ∑n=1∞ λ(n)φ(|Cn|), where Cn are the Haar-Fourier coefficients of an integrable function, φ(x) (x ≥ 0, φ(0) = 0) is an increasing and concave function, and λ(x) (x ≥ 1) denotes a function satisfying certain easily achievable conditions.

AB - Sufficient conditions are given for the convergence of the series ∑n=1∞ λ(n)φ(|Cn|), where Cn are the Haar-Fourier coefficients of an integrable function, φ(x) (x ≥ 0, φ(0) = 0) is an increasing and concave function, and λ(x) (x ≥ 1) denotes a function satisfying certain easily achievable conditions.

KW - Absolute convergence

KW - Convave function

KW - Haar-system

KW - Power-monotone sequences

UR - http://www.scopus.com/inward/record.url?scp=0036545291&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036545291&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0036545291

VL - 5

SP - 263

EP - 269

JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

SN - 1331-4343

IS - 2

ER -