  We prove sharp $L^p$ regularity results for a class of generalized Radon
transforms for families of curves in a three-dimensional manifold associated to
a canonical relation with fold and blowdown singularities. The proof relies on
decoupling inequalities by Wolff and Bourgain-Demeter for plate decompositions
of thin neighborhoods of cones and $L^2$ estimates for related oscillatory
integrals.
