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.
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