Philip GressmanVillano, Dominick2023-05-222001-01-012019-08-272019-01-012019-08-27https://repository.upenn.edu/handle/20.500.14332/30370We 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.53 p.application/pdfDominick VillanoHarmonic AnalysisMathematicsDissertation/Thesis