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Absolute Riesz summability of a Fourier related series, II

Published online by Cambridge University Press:  17 April 2009

G.D. Dikshit
G.D. Dikshit
Affiliation:
Department of Mathematics and Statistics, University of Auckland, Private Bag, Auckland, New Zealand.
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Abstract

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This paper is an endeavour to improve upon the work begun in an earlier paper with the same title. We prove a general theorem on the summability |R, exp((log ω)β+1), ρ| of the series ∑ {sn(x)−s}/n, where {sn(x)} is the sequence of partial sums at a point x of the Fourier series of a Lebesgue integrable 2π-periodic function and s is a suitable constant. While the theorem improves upon the main result contained in the previous paper, corollaries to it include recent results due to Chandra and Yadava.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 1 , August 1985 , pp. 93 - 102
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Chandra, Prem and Yadava, V.S., “On the absolute Riesz summability of series associated with Fourier series”, Indian J. Math. 22 (1980), 105–111.Google Scholar
[2]Chandrasekharan, K. and Minakshisundaram, S., Typical means (Oxford University Press, Oxford, 1952).Google Scholar
[3]Dikshit, G.D., “Absolute Riesz summability of a Fourier related sereis, I”, Math. Japon 30 (1985), 647–658.Google Scholar
[4]Kuttner, B., “On the ‘Second Theorem of Consistency’ for absolute Riesz summability”, Proc. London Math. Soc. (3) 29 (1974), 17–32.CrossRefGoogle Scholar