Sufficient conditions for the Inversion Formula for the $k$-plane Radon Transform in $\mathsf R^n$

Abstract

The inversion theorem (1) for the $k$-plane Radon transform in ${\mathsf R}^n$ is often stated for Schwartz functions, and lately for smooth functions on ${\mathsf R}^n$ fulfilling that $f(x)=O(|x|^{-N})$ for some $N>n$, cf. [6]. In this paper it will be shown, that it suffices to require that $f$ is locally Hölder continuous and $f(x)=O(|x|^{-N})$ for some $N>k$ ($N$ not necessarily an integer) in order for (1) to hold, and that the same decay on $f$ but $f$ only continuous implies an inversion formula only slightly weaker than (1).