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Some integrability theorems

Published online by Cambridge University Press:  18 May 2009

Yung-Ming Chen
Yung-Ming Chen
Affiliation:
Department of MathematicsUniversity of Hong Kong
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 2 , July 1965 , pp. 101 - 108
Copyright
Copyright © Glasgow Mathematical Journal Trust 1965

References

REFERENCES

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