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Inequalities between the integral means of a function
Published online by Cambridge University Press: 17 April 2009
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.
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- Copyright © Australian Mathematical Society 1990
References
[1]Hardy, G.H., Littlewood, J.E. and Polya, G., Inequalities (Cambridge University Press, Cambridge, 1983).Google Scholar
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