Smoothing theorems for Radon transforms over hypersurfaces and related operators

We extend the theorems of [M. Greenblatt, L^{p} Sobolev regularity of averaging operators over hypersurfaces and the Newton polyhedron, J. Funct. Anal. 276 2019, 5, 1510–1527] on {L^{p}} to {L^{p}_{s}} Sobolev improvement for translation invariant Radon and fractional singular Radon transforms over hypersurfaces, proving {L^{p}} to {L^{q}_{s}} boundedness results for such operators. Here {q\geq p} but s can be positive, negative, or zero. For many such operators we will have a triangle {Z\subset(0,1)\times(0,1)\times{\mathbb{R}}} such that one has {L^{p}} to {L^{q}_{s}} boundedness for {({1\over p},{1\over q},s)} beneath Z, and in the case of Radon transforms one does not have {L^{p}} to {L^{q}_{s}} boundedness for {({1\over p},{1\over q},s)} above the plane containing Z, thereby providing a Sobolev space improvement result which is sharp up to endpoints for {({1\over p},{1\over q})} below Z. This triangle Z intersects the plane {\{(x_{1},x_{2},x_{3}):x_{3}=0\}}, and therefore we also have an {L^{p}} to {L^{q}} improvement result that is also sharp up to endpoints for certain ranges of p and q.