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Carlson type inequalities for finite sums and integrals on bounded intervals

Published online by Cambridge University Press:  17 April 2009

Leo Larsson ,
Zsolt Páles  and
Lars-Erik Persson
Leo Larsson
Affiliation:
Department of Mathematics, Uppsala University, Box 480, SE-791 06 Uppsala, Sweden, e-mail: leo@math.uu.se
Zsolt Páles
Affiliation:
Institute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen Pf. 12, Hungary, e-mail: pales@math.klte.hu
Lars-Erik Persson
Affiliation:
Department of Mathematics, Luleå University, SE-971 87 LULEÅ, Sweden and Department of Mathematics, Uppsala University, Box 480, SE-791 06 UPPSALA, Sweden, e-mail: larserik@sm.luth.se
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 2 , April 2005 , pp. 275 - 284
Copyright
Copyright © Australian Mathematical Society 2005

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