This is an announcement for the paper "On the Funk-Radon-Helgason inversion method in integral geometry" by Boris Rubin. Abstract: The paper deals with totally geodesic Radon transforms on constant curvature spaces. We study applicability of the historically the first Funk-Radon-Helgason method of mean value operators to reconstruction of continuous and $L^p$ functions from their Radon transforms. New inversion formulas involving Erd\'elyi-Kober type fractional integrals are obtained. Particular emphasis is placed on the choice of the differentiation operator in the spirit of the recent Helgason's formula. Archive classification: math.FA Mathematics Subject Classification: 44A12 Remarks: 29 pages Submitted from: borisr@math.lsu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.5178 or http://arXiv.org/abs/1207.5178