Weighted norm inequalities for k-plane transforms

TL;DR

This paper derives precise weighted norm inequalities for various k-plane transforms, explicitly calculating operator norms and discussing potential generalizations and open questions in the field.

Contribution

It provides sharp weighted inequalities and explicit operator norm evaluations for k-plane transforms and their duals, advancing understanding of their behavior on weighted L^p spaces.

Findings

Explicit operator norms for k-plane transforms

Sharp weighted inequalities established

Discussion of generalizations and open problems

Abstract

We obtain sharp inequalities for the k-plane transform, the "j-plane to k-plane" transform, and the corresponding dual transforms, acting on $L^p$ spaces with a radial power weight. The operator norms are explicitly evaluated. Some generalizations and open problems are discussed.