LAUSR

Abstract. We define a parametric Radon transform R that assigns to a Sobolev function on the cylinderS×R in R3 its mean values along sets Eζ formed by the intersections of planes through the origin and the cylinder. We show that R is a continuous operator, prove an inversion formula, provide a support theorem, as well as a characterization of its null space. We conclude by presenting a formula for the dual transform R∗. We show that R and its dual R∗ are related to the right-sided and left-sided Chebyshev fractional integrals. Using this relationship, we characterize the null space of R and R∗ and provide an inversion formula for R∗.