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
Recommended Citation
Rubin, B. (2023). On the hemispherical transform in the half-space and related Radon transforms. Analysis and Applications, 21 (4), 1001-1012. https://doi.org/10.1142/S0219530523500082