Abstract

We present a brief discussion of the interrelations between integral geometry and harmonic analysis and then proceed to the d-dimensional totally geodesic Radon transform f, assuming fiELp(Hn), where Hn is the n-dimensional real hyperbolic space, and 1 iU d iU n - 1. We show that f is well defined if and only if 1 iU p < (n -1)/(d - 1) and prove estimates of the Solmon type. By making use of the convolution-backprojection method, approximation to the identity, and the corresponding wavelet-like transforms, we obtain new approximate and explicit inversion formulas for f.

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