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Hardy’s inequality for averages

Published online by Cambridge University Press:  16 February 2023

G. J. O. Jameson
G. J. O. Jameson*
Affiliation:
13 Sandown Road, Lancaster LA1 4LN e-mail: pgjameson@talktalk.net
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The prolific output of G. H. Hardy included a number of inequalities, each known, in its own context, simply as ‘Hardy’s inequality’. Here we give an account of one of them, together with some applications and generalisations. It relates to averages.

Type
Articles
Information
The Mathematical Gazette , Volume 107 , Issue 568 , March 2023 , pp. 25 - 34
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Copyright
© The Authors, 2023. Published by Cambridge University Press on behalf of The Mathematical Association

References

Hardy, G. H., Littlewood, J. and Pólya, G., Inequalities (2nd edn.), Cambridge University Press (1967).Google Scholar
Sinnamon, Gord, Norm of the discrete Cesàro operator minus identity, Math. Ineq. Appl. 25 (2022) pp. 41–48.Google Scholar
Kaiblinger, N., Maligranda, L. and Persson, L.-E., Norms in weighted L 2 - spaces and Hardy operators, in Function spaces, the fifth conference, Poznań 1998, Lecture Notes in Pure Appl. Math. 213 (2000) pp. 205–216.Google Scholar
Brown, A., Halmos, P. R. and Shields, A. L., Cesàro operators, Acta Sci. Math. 26 (1965) pp. 125–137.Google Scholar
Jameson, G. J. O., An equality underlying Hardy’s inequality, Amer. Math. Monthly 129 (2022) pp. 582–586.CrossRefGoogle Scholar
Bennett, G., Inequalities complimentary to Hardy, Quart. J. Math. Oxford 49(2) (1998) pp. 395–432.CrossRefGoogle Scholar
Cartlidge, J. M., Weighted mean matrices as operators on l p, Ph.D. thesis, Indiana University (1978).Google Scholar
Gao, Peng, On a result of Cartlidge, J. Math. Anal. Appl. 332 (2007) pp. 1477–1481.CrossRefGoogle Scholar
Jameson, G. J. O., Some generalisations of Hardy’s inequality: the theorems of Bennett and Cartlidge, accessed August 2022 at www.maths.lancs.ac.uk/˜jameson/genhardy.pdfGoogle Scholar