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Some integrability theorems
Published online by Cambridge University Press: 18 May 2009
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1. P. Heywood [3] proved the following theorems:
Theorem A. If 0 ≦ λ < 2, if xy−1g(x) ε L(0, π), and if
for n = 1, 2, 3,…, then the seriesis convergent.
Theorem B. If 0 ≦ λ < 1, if xy−1f(x)ε L(0, π), and if
for n = 1, 2, 3,…, then the seriesn−yanis convergent.
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- Copyright © Glasgow Mathematical Journal Trust 1965