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Inequalities between the integral means of a function

Published online by Cambridge University Press:  17 April 2009

D. Hajela
D. Hajela
Affiliation:
Bellcore445 South StreetMorristown, NJ 07960United States of America
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Abstract

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For a measurable function f on a probability space a basic inequality is ‖f‖p ≤ ‖f‖q where 1 ≤ p < q < ∞ and ‖f‖p denotes the Lp norm of f. The above inequality becomes an equality provided |f| is a constant almost everywhere. We obtain an improvement of the above inequality in all cases that |f| is not a constant almost everywhere.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 2 , April 1990 , pp. 245 - 248
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Hardy, G.H., Littlewood, J.E. and Polya, G., Inequalities (Cambridge University Press, Cambridge, 1983).Google Scholar
[2]Mitronovic, D.S., Analyic Inequalities (Springer-Verlag, Berlin, Heidelberg, New York, 1970).CrossRefGoogle Scholar