Sufficient Conditions for the Inversion Formula for the k-plane Radon Transform in R^n

Abstract

The inversion theorem for the k-plane Radon transform in R^n is often stated for Schwartz functions, and lately for smooth functions on R^n fulfilling that f(x)=O(|x|^{-N}) for some N>n. In this paper it will be shown, that it suffices to require that f is locally Holder continuous and f(x)=O(|x|^{-N}) for some N>k (N not necessarily an integer), and that a slightly weaker inversion formula holds when f with the same decay as before is only continuous.