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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Necessary and sufficient conditions for $ L\sp{1}$ convergence of trigonometric series


Authors: John W. Garrett and Časlav V. Stanojević
Journal: Proc. Amer. Math. Soc. 60 (1976), 68-71
MSC: Primary 42A20
MathSciNet review: 0425480
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Abstract: It is shown that for the class of cosine series satisfying $ a(n)\log n = o(1)$ and $ \Delta a(n) \geqslant 0$ that integrability and $ {L^1}$ convergence occur together. Relaxing the monotonicity to bounded variation we show that our previous result cannot be extended.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0425480-3
Keywords: $ {L^1}$ convergence of Fourier series, Fejér sums
Article copyright: © Copyright 1976 American Mathematical Society