Operator identities relating sonar and Radon transforms in Euclidean space

A Note on the Sonar Transform and Related Radon Transforms

The sonar transform in geometric tomography maps functions on the Euclidean half-space to integrals of those functions over hemispheres centered on the boundary hyperplane. We obtain sharp $L^p$-$L^q$ estimates for this transform and new explicit inversion formulas under minimal assumptions for functions. The main results follow from intriguing connection between the sonar transform, the Radon transform over paraboloids, and the transversal Radon transform, which integrates functions over hyperplanes, meeting the last coordinate axis.

利用常规Radon变换逆解迁移成像中出现的椭圆Radon变换

Inversion of the elliptical Radon transform arising in migration imaging using the regular Radon transform

本文研究了在迁移成像中出现的椭圆Radon变换，通过与常规Radon变换的关系推导了其逆变换公式，并通过二维数值模拟验证了算法有效性。

$\nmathbb{R}^n$ 中广义曲面上的旋转曲面 Radon 变换

Surface of revolution Radon transforms with centers on generalized surfaces in $\mathbb{R}^n$

本文分析 $\nmathbb{R}^n$ 中广义曲面上的旋转曲面 Radon 变换，推导 Bolker 条件充要条件，提出基于 Volterra 方程的反演框架并证明单射性，应用于 CST 和 URT，通过模拟验证理论。

Good lambda inequalities for non-doubling measures in $\mathbb{R}^n$

We establish a good lambda inequality relating to the distribution function of Riesz potential and fractional maximal function on $\left(\mathbb{R}^n, dμ\right)$ where $μ$ is a positive Radon measure which doesn't necessarily satisfy a doubling condition. This is extended to weights $w$ in $A_{\infty}(μ)$ associated to the measure $μ$. We also derive potential inequalities as an application.