Quantitative form of certain k-plane transform inequalities

2012/05/15 by Drouot, Alexis
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1205.3251

Abstract

Let d > 1 and 0 < k < d. The k-plane transform satisies some Lp to Lq dilation-invariant inequality. In this case the best constant and the extremizers are explicitly known. We give a quantitative form of the inequality with respect to these extremizers, that works for k = d - 1 and for k < d-1 while restricted to radial functions.

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