Hostname: page-component-5db58dd55d-xnzfm Total loading time: 0 Render date: 2026-05-25T18:19:51.526Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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.

Information

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

1.Boas, R. P. Jr, Integrability of trigonometric series (III). Quart. J. Math. Oxford Ser. (2) 3 (1952), 217–221.CrossRefGoogle Scholar
2.Chen, Y. M., On two functional spaces, Studia Math. 24 (1964), 61–88.CrossRefGoogle Scholar
3.Heywood, P., Integrability theorems for trigonometric series, Quart. J. Math. Oxford Ser. (2) 13 (1962), 172–180.CrossRefGoogle Scholar
4.Karamata, J., Sur un mode de croissance regulière des fonctions, Mathematica (Cluj) 4 (1930), 38–53.Google Scholar
5.Karamata, J., Sur un mode de croissance regulière, Bull. Soc. Math, de France 61 (1933), 55–62.CrossRefGoogle Scholar
6.O'Shea, Siobhan, Note on an integrability theorem for sine series, Quart. J. Math. Oxford Ser. (2) 8 (1957), 279–281.CrossRefGoogle Scholar
7.Zygmund, A., Trigonometric series, 2nd edn, Vol. 1 (Cambridge, 1959).Google Scholar