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 | References | Similar Articles | Additional Information

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

Received by editor(s):
June 12, 2003

Published electronically:
June 16, 2004

Communicated by:
Andreas Seeger

Article copyright:
© Copyright 2004
American Mathematical Society