Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-27T23:18:22.297Z Has data issue: false hasContentIssue false
  • English
  • Français

A SHARP VERSION OF BONSALL’S INEQUALITY

Part of: Integral transforms, operational calculus

Published online by Cambridge University Press:  19 August 2015

T. C. PEACHEY
T. C. PEACHEY*
Affiliation:
Research Computing Centre, University of Queensland, St. Lucia, Queensland 4072, Australia email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

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.

The best possible constant in a classical inequality due to Bonsall is established by relating that inequality to Young’s. Further, this extends the range of Bonsall’s inequality and yields a reverse inequality. It also provides a better constant in an inequality of Hardy, Littlewood and Pólya.

Keywords

Bonsall’s inequalityconvolutionYoung’s inequalitySchur’s inequality

MSC classification

Secondary: 44A35: Convolution
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 3 , December 2015 , pp. 397 - 404
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Beckner, W., ‘Inequalities in Fourier analysis’, Ann. of Math. (2) 102 (1975), 159–182.CrossRefGoogle Scholar
Bonsall, F. F., ‘Inequalities with non-conjugate parameters’, Q. J. Math. 2 (1951), 135–150.CrossRefGoogle Scholar
Brascamp, H. J. and Lieb, E. H., ‘Best constants in Young’s inequality, its converse, and its generalization to more than three functions’, Adv. Math. 20 (1976), 151–173.CrossRefGoogle Scholar
Erdélyi, A., ‘An extension of a Hardy–Littlewood–Polya inequality’, Proc. Edinb. Math. Soc. (2) 21 (1978), 11–15.CrossRefGoogle Scholar
Finch, S. R., Mathematical Constants (Cambridge University Press, Cambridge, 2003).Google Scholar
Hardy, G. H., Littlewood, J. E. and Pólya, G., Inequalities, 2nd edn (Cambridge University Press, Cambridge, 1952).Google Scholar
Levin, V., ‘On the two parameter extension and analogue of Hilbert’s inequality’, J. Lond. Math. Soc. (2) 11 (1936), 119–124.CrossRefGoogle Scholar
Peachey, T. C., ‘Some inequalities related to Hilbert’s’, J. Inequal. Pure Appl. Math. 4(1) (2003), Art. 19.Google Scholar
Peachey, T. C. and Enticott, C. M., ‘Determination of the best constant in an inequality of Hardy, Littlewood, and Pólya’, Exp. Math. 15(1) (2006), 43–50.CrossRefGoogle Scholar
Young, W. H., ‘On the multiplication of successions of Fourier constants’, Proc. Roy. Soc. A 87(596) (1912), 331–339.Google Scholar