Restricted Radon Transforms and Unions of Hyperplanes

Abstract

We study $L^p({\mathbb{R}}^n)\to L_{d\mu (\sigma )}^{\alpha ,\infty }(L_{dt}^{\infty })$ estimates for the Radon transform in certain cases where the dimension of the measure $\mu$ on ${\Sigma }^{(n-1)}$ is less than $n-1$.