## Hokkaido Mathematical Journal

### On the generalized absolute convergence of Fourier series

László LEINDLER

#### Abstract

Sufficient conditions are given by means of the best trigonometric approxi- mation in $L^{p}(1<p\leq 2)$ and structural properties of $f\in L^{p}$ for the convergence of the series $$\sum_{n=1}^{\infty}\omega_{n}(\varphi(|a_{n}|)+\varphi(|b_{n}|)) ,$$ where $a_{n}$ and $b_{n}$ are the Fourier coefficients of $f$, $\{\omega_{n}\}$ is a certain sequence of positive numbers, $\varphi(u)(u\geq 0)$ denotes an increasing concave function.

#### Article information

Source
Hokkaido Math. J., Volume 30, Number 1 (2001), 241-251.

Dates
First available in Project Euclid: 22 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1350911935

Digital Object Identifier
doi:10.14492/hokmj/1350911935

Mathematical Reviews number (MathSciNet)
MR1815892

Zentralblatt MATH identifier
1002.42004

#### Citation

LEINDLER, László. On the generalized absolute convergence of Fourier series. Hokkaido Math. J. 30 (2001), no. 1, 241--251. doi:10.14492/hokmj/1350911935. https://projecteuclid.org/euclid.hokmj/1350911935