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

 

A multilinear generalisation of the Cauchy-Schwarz inequality


Author: Anthony Carbery
Journal: Proc. Amer. Math. Soc. 132 (2004), 3141-3152
MSC (2000): Primary 05A20, 42B99
Published electronically: June 16, 2004
MathSciNet review: 2073287
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Abstract: We prove a multilinear inequality which in the bilinear case reduces to the Cauchy-Schwarz inequality. The inequality is combinatorial in nature and is closely related to one established by Katz and Tao in their work on dimensions of Kakeya sets. Although the inequality is ``elementary" in essence, the proof given is genuinely analytical insofar as limiting procedures are employed. Extensive remarks are made to place the inequality in context.


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Additional Information

Anthony Carbery
Affiliation: School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Edinburgh EH9 3JZ, United Kingdom
Email: A.Carbery@ed.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07565-3
PII: S 0002-9939(04)07565-3
Received by editor(s): June 12, 2003
Published electronically: June 16, 2004
Communicated by: Andreas Seeger
Article copyright: © Copyright 2004 American Mathematical Society