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A sharp inequality related to Moser's inequality

Part of: Real functions

Published online by Cambridge University Press:  26 February 2010

P. C. McCarthy
P. C. McCarthy
Affiliation:
Department of Mathematics, University CollegeCork, Ireland
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Extract

In this paper we shall be concerned with the growth of functions in the class ℳp, where we write f ∈ ℳp 1 <p<∞, if:

(i) f is absolutely continuous on bounded subintervals of [0, ∞]);

(ii) f(0) = 0; and

(iii) .

MSC classification

Secondary: 26A46: Absolutely continuous functions
Type
Research Article
Information
Mathematika , Volume 40 , Issue 2 , December 1993 , pp. 357 - 366
Copyright
Copyright © University College London 1993

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References

1.Carleson, L. and Chang, S.-Y. A.. On the existence of an extremal for an inequality of J. Moser. Bull, des Science, 110 (1986), 113–127.Google Scholar
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4.Marshall, D. E.. A new proof of a sharp inequality concerning the Dirichlet integral. Arkiv. Mat., 27 (1989), 131–137.CrossRefGoogle Scholar
5.Moser, J.. A sharp form of an inequality by N. Trudinger. Ind. V. Math. J., 20 (1971), 1077–1092.CrossRefGoogle Scholar