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Carlson type inequalities for finite sums and integrals on bounded intervals
Published online by Cambridge University Press: 17 April 2009
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We investigate Carlson type inequalities for finite sums, that is, inequalities of the form to hold for some constant C independent of the finite, non-zero set a1,…,am of non-negative numbers. We find constants C which are strictly smaller than the sharp constants in the corresponding infinite series case. Moreover, corresponding results for integrals over bounded intervals are given and a case with any finite number of factors on the right-hand side is proved.
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- Copyright © Australian Mathematical Society 2005