Two endpoint bounds for generalized Radon transforms in the plane

The purpose of this note is to prove Lp! Lqinequalities for averaging operators in the plane(also known as generalized Radon transforms). To describe our setupletLandR be open sets inR2and let M be a submanifoldinLR which will contain the singular support of the kernel ofour operator. We assume that the projections M!L and M!R have surjective dierential;thus the varieties(1.1)M x = fy2R ; (x; y) 2 MgMy= fx2L ; (x; y) 2...