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Rearrangements of affine subspaces in vector spaces over finite fields

Published online by Cambridge University Press:  15 July 2011

Anthony Carbery  and
Daniel Wilheim
Anthony Carbery
Affiliation:
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK ([email protected])
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Abstract

We consider the Lp norms of sums of characteristic functions of affine subspaces of a vector space V over a finite field under certain restrictions on p, dim V and the dimensions of the subspaces involved. We investigate the conditions under which these norms are increased when the affine subspaces are replaced by their parallel translates passing through 0. Applications to extremal configurations for Kakeya maximal-type inequalities are given and open questions are raised.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 4 , August 2011 , pp. 709 - 715
Copyright
Copyright © Royal Society of Edinburgh 2011

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