Date of Award

2019

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Mathematics

First Advisor

Philip Gressman

Abstract

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.

Included in

Mathematics Commons

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