简单连通恒定曲率空间上完全大地拉顿变换的端点估计:统一方法

Aniruddha Deshmukh, Ashisha Kumar
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引用次数: 0

摘要

本文给出了恒曲率空间上径向函数全大地$k$平面变换端点估计的统一证明。获得端点估计的问题并不新鲜,文献中也有一些结果。然而,这些结果都是独立获得的,并不太关注底层几何之间的相似性。我们利用曲率恒定空间共有的几何思想,给出了曲率恒定空间端点估计的统一证明,并得到了径向函数 $k$ 平面变换的统一公式。我们还给出了某些特殊函数的不等式,作为我们的一个定理的应用。
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End-point estimates of the totally-geodesic Radon transform on simply connected spaces of constant curvature: A Unified Approach
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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