Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T01:28:46.878Z Has data issue: false hasContentIssue false
  • English
  • Français

A simpler proof of two inequalities of Brodlie and Everitt

Published online by Cambridge University Press:  14 November 2011

P. R. Beesack
P. R. Beesack
Affiliation:
Carleton University, Ottawa, Canada
Get access Rights & Permissions [Opens in a new window]

Synopsis

In 1975 K. W. Brodie and W. N. Everitt dealt with integral inequalities of the form

in the two cases T = ℝ, T = ℝ+, and obtained the best possible constants KT(μ) for all μ ε ℝ. The proof was not elementary, but an elementary proof was given in 1977 by E. T. Copson. This note shows how Copson's method can be greatly simplified so as to obtain the results in a more straightforward manner.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 3-4 , 1979 , pp. 259 - 261
Copyright
Copyright © Royal Society of Edinburgh 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Brodlie, K. W. and Everitt, W. N.. On an inequality of Hardy and Littlewood. Proc. Roy. Soc. Edinburgh Sect. A 72 (1975), 179–186.Google Scholar
2Copson, E. T.. On two inequalities of Brodlie and Everitt. Proc. Roy. Soc. Edinburgh Sect. A 77 (1977), 329–333.CrossRefGoogle Scholar
3Copson, E. T.. On two integral inequalities. Proc. Roy. Soc. Edinburgh Sect. A 77 (1977), 325–328.Google Scholar
4Hardy, G. H., Littlewood, J. E., and Pólya, G.. Inequalities, 2nd edn (Cambridge Univ. Press, 1952).Google Scholar