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12.—On an Inequality of Hardy and Littlewood*

Published online by Cambridge University Press:  14 February 2012

K. W. Brodlie  and
W. N. Everitt
K. W. Brodlie
Affiliation:
Department of Mathematics, University of Dundee
W. N. Everitt
Affiliation:
Department of Mathematics, University of Dundee
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Extract

This paper considers a natural extension of the following inequality of Hardy and Littlewood

to an inequality of the form

where μ>0 and 0<K(μ)<∞. The best possible value of k(μ) is determined, and all the cases of equality.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 72 , Issue 3 , 1975 , pp. 179 - 186
Copyright
Copyright © Royal Society of Edinburgh 1975

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References

References to Literature

[1]Everitt, W. N., 1971. On an extension to an integro-differential inequality of Hardy, Littlewood and Polya. Proc. Roy. Soc. Edinb., 69A, 295–333.Google Scholar
[2]Everitt., W. N., 1972. On a property of the m-coefficient of a second-order linear differential equation. J Lond. Math. Soc., 4, 443–457.CrossRefGoogle Scholar
[3]Hardy, G. H. and Littlewood, J. E., 1932. Some integral inequalities connected with the calculus of variations. Q. Jl Math., 3, 241–252CrossRefGoogle Scholar
[4]Hardy, G. H.Littlewood, J. E. and Polya, G. 1934. Inequalities. C.U.P.Google Scholar
[5]Kallman, R. R. and Rota, G.-C. 1970. On the inequality ‖f′‖2≦4‖f‖‖f″ ‖. In Inequalities II (Shisha, Oved, Ed.), 187–192.New York and London: Academic Press.Google Scholar
[6]Kato, T., 1971. On an inequality of Hardy, Littlewood and Polya. Adv. Math., 7, 217–218.CrossRefGoogle Scholar
[7]Ljubic, Ju. I. (or Lyubich), 1960. On inequalities between the powers of a linear operator. Izv. Akad. Nauk. SSSR Ser. Mat., 24, 825–864. (Translated from the Russian in Transl. Amer. Math. Soc, 40, 1964, 39–84).Google Scholar
[8]Redheffer, R. M. 1963. Uber eine beste Ungleichung zwischen den Normen vonf,f′,f″, Math. Z., 80, 390–397.CrossRefGoogle Scholar
[9]Dunford, N. and Schwartz, J. T., 1963. Linear operators, II. New York and London: Interscience.Google Scholar