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February 2001 On the generalized absolute convergence of Fourier series
László LEINDLER
Hokkaido Math. J. 30(1): 241-251 (February 2001). DOI: 10.14492/hokmj/1350911935

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.

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László LEINDLER. "On the generalized absolute convergence of Fourier series." Hokkaido Math. J. 30 (1) 241 - 251, February 2001. https://doi.org/10.14492/hokmj/1350911935

Information

Published: February 2001
First available in Project Euclid: 22 October 2012

zbMATH: 1002.42004
MathSciNet: MR1815892
Digital Object Identifier: 10.14492/hokmj/1350911935

Subjects:
Primary: 42A28
Secondary: 42A16

Rights: Copyright © 2001 Hokkaido University, Department of Mathematics

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Vol.30 • No. 1 • February 2001
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