Strichartz’s Radon transforms for mutually orthogonal affine planes and fractional integrals

Abstract

In this paper, we study the general orthogonal Radon transform $${R}_{j,k}^p$$ first studied by R.S. Strichartz in [21]. The main conclusions include the sharp existence conditions for $${R}_{j,k}^pf$$ on Lebesgue spaces, the relation formulas connecting our transforms with the fractional integrals and Semyanistyi integrals, through which a number of explicit inversion formulas are obtained when f restricted in the range of j-plane transforms.