Date of Award
Doctor of Philosophy (PhD)
We prove \(L^p-L^q\) boundedness for a wide class of Radon-like transforms. The technique of proof leverages the existing one-dimensional theory to produce a non-trivial bounds in any dimension. For certain combinatorially simple transforms, this range is sharp up to endpoints. Additionally, we make observations connecting the \(L^p\)-improving properties of a Radon-like transform to the zero set of certain homogeneous polynomials.
Villano, Dominick, "Some \(l^p\)-Improving Bounds For Radon-Like Transforms" (2019). Publicly Accessible Penn Dissertations. 3356.