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On the absolute Nörlund summability factors of a Fourier series and its conjugate series at a point

Published online by Cambridge University Press:  17 April 2009

Kôsi Kanno
Kôsi Kanno
Affiliation:
Mathematical Institute, Yamagata University, Yamagata, Japan.
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Abstract

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The object of this paper is to give generalizations of Okuyama's Theorem [Bull. Austral. Math. Soc.12 (1975), 9–21, Tôohoku Math. J. (2) 28 (1976), 563–581] on the absolute Nörlund summability factors of a Fourier series and its conjugate series.

Our theorems imply many results proved by other authors: especially Theorem 1 includes the results of Bhatt and Kishor [Indian J. Math.9 (1967), 259–267 (1968)], Dikshit [Pacific J. Math.63 (1976), 371–379], and Lal [Publ. Inst. Math. (Beograd) 20 (34) (1976), 169–178], and we can easily deduce Lal's result [Indian J. Math.16 (1974), 1–22] from our Corollary 2.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 2 , October 1978 , pp. 161 - 181
Copyright
Copyright © Australian Mathematical Society 1979

References

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