Vol. 7, No. 6, 2014

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Sharp constant for a $k$-plane transform inequality

Alexis Drouot

Vol. 7 (2014), No. 6, 1237–1252
Abstract

The k-plane transform k acting on test functions on d satisfies a dilation-invariant Lp Lq inequality for some exponents p,q. We will make explicit some extremizers and the value of the best constant for any value of k and d, solving the endpoint case of a conjecture of Baernstein and Loss. This extends their own result for k = 2 and Christ’s result for k = d 1.

Keywords
k-plane transform, best constant, extremizers
Mathematical Subject Classification 2010
Primary: 44A12
Milestones
Received: 27 January 2012
Revised: 3 June 2014
Accepted: 27 August 2014
Published: 18 October 2014
Authors
Alexis Drouot
Department of Mathematics
UC Berkeley
Berkeley, 94704
United States