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ON WEIGHTED INEQUALITIES WITH GEOMETRIC MEAN OPERATOR

Part of: Inequalities

Published online by Cambridge University Press:  01 December 2008

DAH-CHIN LUOR
DAH-CHIN LUOR*
Affiliation:
Department of Applied Mathematics, I-Shou University, Ta-Hsu, Kaohsiung 84008, Taiwan (email: dclour@isu.edu.tw)
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Abstract

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We give a characterization of pairs of weights for the validity of weighted inequalities involving certain generalized geometric mean operators generated by some Volterra integral operators, which include the Hardy averaging operator and the Riemann–Liouville integral operators. The estimations of the constants are also discussed. Our results generalize the work done by J. A. Cochran, C.-S. Lee, H. P. Heinig, B. Opic, P. Gurka, and L. Pick.

Keywords

geometric mean operatorintegral operatorweighted inequalityexponential inequality

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 3 , December 2008 , pp. 463 - 475
Copyright
Copyright © 2009 Australian Mathematical Society

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