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Absolute Riesz summability of Fourier series and their conjugate series

Published online by Cambridge University Press:  17 April 2009

Masako Izumi  and
Shin-ichi Izumi
Masako Izumi
Affiliation:
Department of Mathematics, Institute of Advanced Studies, The Australian National University, Canberra, ACT.
Shin-ichi Izumi
Affiliation:
Department of Mathematics, Institute of Advanced Studies, The Australian National University, Canberra, ACT.
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Abstract

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This paper contains two theorems. The first theorem treats the |R, r, l| summability of Fourier series and their associated series of functions of bounded variation. The second concerns the |R, r, l| summability of Fourier series of functions f such that φ(t)m(l/t) is of bounded variation where m(u) increases to infinity as u → ∞. These theorems generalize Mohanty's theorems.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 2 , October 1970 , pp. 217 - 229
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Mohanty, R., “On the absolute Riesz simmability of Fourier series and allied series”, Proc. London Math. Soc. (2) 52 (1951), 295–320.Google Scholar
[2]Izumi, Shin-ichi and Satô, Masako (= Masako Izumi), “Integrability of trigonometric series. I”, Tôhoku Math. J. (2) 6 (1954), 258–263.Google Scholar