Existence and non-existence of extremizers for certain $k$-plane transform inequalities

Abstract

We provide sharp forms of $k$-plane transform inequalities on the $d$-dimensional sphere ${\mathbb{S}}^d$ and the $d$-dimensional hyperbolic space ${\mathbb{H}}^d$. In particular, we prove that extremizers do not exist for ${\mathbb{H}}^d$. This work is a natural extension of some results for the $k$-plane transform on ${\mathbb{R}}^d$.

11 pages

References in corpus (3)

• Quasiextremals for a Radon-like transform
• On extremals for a Radon-like transform
• Best constant and value of extremizers for a k-plane transform inequality