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On the Behaviour of a Series Associated with the Conjugate Series of a Fourier Series
Published online by Cambridge University Press: 20 November 2018
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1.1. Definition. Let λ ≡ λ(ω) be continuous, differentiable, and monotonic increasing in (0, ∞) and let it tend to infinity as ω → ∞. Suppose that ∑ an (we write ∑ for throughout the present paper) is a given infinite series and let
The series ∑ an is said to be summable |R, λ, r|, where r > 0, if
where A is a fixed positive number (6, Definition B). Now, for r > 0, m < ω < m + 1,
Hence, ∑ an is summable |R, λ, r|, where r > 0, if
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- Copyright © Canadian Mathematical Society 1969
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