RADON TRANSFORMS OVER LOWER-DIMENSIONAL HOROSPHERES IN REAL HYPERBOLIC SPACE

摘要

We study horospherical Radon transforms that integrate functions on the n-dimensional real hyperbolic space over horospheres of arbitrary fixed dimension 1 `<= d <= n-1. Exact existence conditions and new explicit inversion formulas are obtained for these transforms acting on smooth functions and functions belonging to L-p. The case d = n - 1 agrees with the well-known Gelfand-Graev transform.