# [Banach] Abstract of a paper by David Alonso-Gutierrez

Dale Alspach alspach at www.math.okstate.edu
Sun Nov 4 08:06:30 CST 2007

This is an announcement for the paper "On an extension of the
Blaschke-Santalo inequality" by David Alonso-Gutierrez.

Abstract: Let $K$ be a convex body and $K^\circ$ its polar body.
Call $\phi(K)=\frac{1}{|K||K^\circ|}\int_K\int_{K^\circ}\langle x,y\rangle^2 dxdy$.  It is conjectured that $\phi(K)$ is maximum
when $K$ is the euclidean ball. In particular this statement implies
the Blaschke-Santalo inequality. We verify this conjecture when $K$
is restricted to be a $p$--ball.

Archive classification: math.FA

Mathematics Subject Classification: 52A20; 52A40; 46B20

Remarks: 7 pages

The source file(s), p-balls5.tex: 18249 bytes, is(are) stored in
gzipped form as 0710.5907.gz with size 6kb. The corresponding
postcript file has gzipped size 65kb.

Submitted from: 498220 at celes.unizar.es

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http://front.math.ucdavis.edu/0710.5907

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http://arXiv.org/abs/0710.5907

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