On the hemispherical transform in the half-space and related Radon transforms

Document Type

Article

Publication Date

7-1-2023

Abstract

We consider an integral transform which maps functions on the Euclidean half-space to integrals of these functions over hemispheres centered on the boundary hyperplane. The main results include sharp Lp-Lq estimates for this transform and new explicit inversion formulas under minimal assumptions for functions. The main idea is an intriguing connection between the hemispherical transform, the Radon transform over paraboloids, and the transversal Radon transform over hyperplanes meeting the last coordinate axis.

Publication Source (Journal or Book title)

Analysis and Applications

First Page

1001

Last Page

1012

This document is currently not available here.

Share

COinS