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

2014/12/16 by Drouot, Alexis
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1412.4876

Abstract

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

Related

• Uniqueness of extremizers for an endpoint inequality of the k-plane transform
• Extremizers of a Radon transform inequality
• Smoothness of extremizers for certain inequalities of the Radon transform
• Quantitative form of certain k-plane transform inequalities
• Overdetermined Transforms in Integral Geometry