A multilinear generalisation of the Cauchy-Schwarz inequality
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- by Anthony Carbery
- Proc. Amer. Math. Soc. 132 (2004), 3141-3152
- DOI: https://doi.org/10.1090/S0002-9939-04-07565-3
- Published electronically: June 16, 2004
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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.References
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Bibliographic 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
- Received by editor(s): June 12, 2003
- Published electronically: June 16, 2004
- Communicated by: Andreas Seeger
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3141-3152
- MSC (2000): Primary 05A20, 42B99
- DOI: https://doi.org/10.1090/S0002-9939-04-07565-3
- MathSciNet review: 2073287