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L1-convergence of Fourier series

Part of: Harmonic analysis in one variable

Published online by Cambridge University Press:  09 April 2009

Chang-Pao Chen
Chang-Pao Chen
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305, U.S.A.
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Abstract

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For an integrable function f on T, we introduce a modified partial sum and establish its L1-convergence property. The relation between the sum and L1-convergence classes is also established. As a corollary, a new L1-convergence class is obtained. It is shown that this class covers all known L1-convergence classes.

Keywords

L1-convergence of Fourier seriesL1-convergence classes.

MSC classification

Secondary: 42A20: Convergence and absolute convergence of Fourier and trigonometric series 42A32: Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 3 , December 1986 , pp. 376 - 390
Copyright
Copyright © Australian Mathematical Society 1986

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