### Abstract

Very recently S. Yu. Tikhonov proved a theorem which gives a necessary and sufficient condition in order that a function f(x) ∈ L _{p} having quasi-monotone decreasing Fourier coefficients should belong to the Besov-Nikol'skiǐ class. In the present paper the analogue of his result is proved with function having Fourier coefficients of rest bounded variation.

Original language | English |
---|---|

Pages (from-to) | 237-248 |

Number of pages | 12 |

Journal | Publicationes Mathematicae |

Volume | 64 |

Issue number | 1-2 |

Publication status | Published - 2004 |

### Fingerprint

### Keywords

- Besov-Nikol'skiǐ class
- Fourier coefficients
- Inequalities for sums
- Modulus of smoothness
- Sequences of monotone type

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Publicationes Mathematicae*,

*64*(1-2), 237-248.

**A theorem on Besov-Nikol'skiǐ class.** / Leindler, L.

Research output: Contribution to journal › Article

*Publicationes Mathematicae*, vol. 64, no. 1-2, pp. 237-248.

}

TY - JOUR

T1 - A theorem on Besov-Nikol'skiǐ class

AU - Leindler, L.

PY - 2004

Y1 - 2004

N2 - Very recently S. Yu. Tikhonov proved a theorem which gives a necessary and sufficient condition in order that a function f(x) ∈ L p having quasi-monotone decreasing Fourier coefficients should belong to the Besov-Nikol'skiǐ class. In the present paper the analogue of his result is proved with function having Fourier coefficients of rest bounded variation.

AB - Very recently S. Yu. Tikhonov proved a theorem which gives a necessary and sufficient condition in order that a function f(x) ∈ L p having quasi-monotone decreasing Fourier coefficients should belong to the Besov-Nikol'skiǐ class. In the present paper the analogue of his result is proved with function having Fourier coefficients of rest bounded variation.

KW - Besov-Nikol'skiǐ class

KW - Fourier coefficients

KW - Inequalities for sums

KW - Modulus of smoothness

KW - Sequences of monotone type

UR - http://www.scopus.com/inward/record.url?scp=1542351588&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542351588&partnerID=8YFLogxK

M3 - Article

VL - 64

SP - 237

EP - 248

JO - Publicationes Mathematicae

JF - Publicationes Mathematicae

SN - 0033-3883

IS - 1-2

ER -