Lebesgue space bounds for 2-surfaces in convolution and decoupling
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Date
2023
Authors
Meade, Conor
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Publisher
University College Cork
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Abstract
This thesis is a collection of proofs of theorems in the field of Harmonic Analysis. The through-line that connects these theorems is the estimation of L^p norms of operators relating to polynomial 2-surfaces, with the curvature of these surfaces playing a key role in each of the results.
The operators that define these theorems are most generally parameterised by a choice of manifold in R^n. Typically, the cases where the manifold is of dimension 1 or of dimension n-1 have been well studied, but intermediate dimensions remain difficult to obtain results for. In this thesis, we aim to extend techniques used for 1-dimensional manifolds to obtain results for some 2-dimensional manifolds.
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Keywords
Mathematics , Harmonic analysis
Citation
Meade, C. 2023. Lebesgue space bounds for 2-surfaces in convolution and decoupling. PhD Thesis, University College Cork.