Quantitative form of certain k-plane transform inequalities
Classical Analysis and ODEs
2014-11-19 v3
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.
Cite
@article{arxiv.1205.3251,
title = {Quantitative form of certain k-plane transform inequalities},
author = {Alexis Drouot},
journal= {arXiv preprint arXiv:1205.3251},
year = {2014}
}
Comments
31 pages, Journal of Functional Anaysis (2014)