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On the Absolute Cesaro Summability of Negative Order of a Series Associated with the Conjugate Series of a Fourier Series

Published online by Cambridge University Press:  20 November 2018

R. Mohanty  and
B. K. Ray
R. Mohanty
Affiliation:
Ravenshaw College, Cuttack (Orissa), India
B. K. Ray
Affiliation:
Ravenshaw College, Cuttack (Orissa), India
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1. Definition. Let λ ≡ λ(ω) be continuous, differentiable, and monotonie increasing in (0, ∞) and let it tend to infinity as ω → ∞. A series an is summable |R, λ, r|, where r > 0, if

where A is a fixed positive number (6, Definition B).

Let f(t) be a periodic function with period 2π and Lebesgue integrable over (–π, π) and let

1.1

The series conjugate to (1.1), at t = x, is

1.2

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 552 - 557
Copyright
Copyright © Canadian Mathematical Society 1969

References

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