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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mixed means and inequalities of Hardy
and Levin-Cochran-Lee type
for multidimensional balls


Authors: Aleksandra Cizmesija, Josip Pecaric and Ivan Peric
Journal: Proc. Amer. Math. Soc. 128 (2000), 2543-2552
MSC (2000): Primary 26D10, 26D15
Published electronically: December 7, 1999
MathSciNet review: 1676291
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Abstract | References | Similar Articles | Additional Information

Abstract: Integral means of arbitrary order, with power weights and their companion means, where the integrals are taken over balls in $\mathbf{ R}^n$ centered at the origin, are introduced and related mixed-means inequalities are derived. These relations are then used in obtaining Hardy and Levin-Cochran-Lee inequalities and their companion results for $n$-dimensional balls. Finally, the best possible constants for these inequalities are obtained.


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Additional Information

Aleksandra Cizmesija
Affiliation: Department of Mathematics, University of Zagreb, Bijeničkacesta 30, 10000 Zagreb, Croatia
Email: cizmesij@math.hr

Josip Pecaric
Affiliation: Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia
Email: pecaric@mahazu.hazu.hr

Ivan Peric
Affiliation: Faculty of Chemical Engineering and Technology, University of Zagreb, Marulićev trg 19, 10000 Zagreb, Croatia

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05408-8
PII: S 0002-9939(99)05408-8
Keywords: Mixed means, Hardy inequality, Levin--Cochran--Lee inequality
Received by editor(s): September 28, 1998
Published electronically: December 7, 1999
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2000 American Mathematical Society