Weighted norm inequalities for $k$-plane transforms

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.

Locations

• Proceedings of the American Mathematical Society - View - PDF
• arXiv (Cornell University) - View - PDF