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On an inequality of Hardy-Littlewood type: I

Published online by Cambridge University Press:  14 November 2011

W. D. Evans  and
W. N. Everitt
W. D. Evans
Affiliation:
Department of Pure Mathematics, University College, Cardiff CF1 1XL, Wales
W. N. Everitt
Affiliation:
Department of Mathematics, University of Birmingham, Birmingham B15 2TT, England
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Synopsis

This paper gives a complete analysis of the integral inequality

where the integral on the left may be only conditionally convergent. It is shown that the best possible number K is 4 and all cases of equality are identified in terms of Hankel-Bessel functions of order ⅓.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 1-2 , 1985 , pp. 131 - 140
Copyright
Copyright © Royal Society of Edinburgh 1985

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