Quantitative form of certain k-plane transform inequalities

摘要

Let d >= 2 and 1 <= k <= d - 1. The k-plane transform satisfies some L-p -> L-q 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 not equal d - 1 while restricted to radial functions. (C) 2014 Elsevier Inc. All rights reserved.