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arXiv · 2408.13541

End-point estimates of the totally-geodesic Radon transform on simply connected spaces of constant curvature: A Unified Approach

Aniruddha Deshmukh·Ashisha Kumar
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Abstract

In this article, we give a unified proof of the end-point estimates of the totally-geodesic $k$-plane transform of radial functions on spaces of constant curvature. The problem of getting end-point estimates is not new and some results are available in literature. However, these results were obtained independently without much focus on the similarities between underlying geometries. We give a unified proof for the end-point estimates on spaces of constant curvature by making use of geometric ideas common to the spaces of constant curvature, and obtaining a unified formula for the $k$-plane transform of radial functions. We also give some inequalities for certain special functions as an application to one of our lemmata.

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Aniruddha Deshmukh, Ashisha Kumar. 2024-08-24. End-point estimates of the totally-geodesic Radon transform on simply connected spaces of constant curvature: A Unified Approach. https://doi.org/10.1080/10652469.2025.2536170

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