Lebesgue space bounds for 2-surfaces in convolution and decoupling

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dc.contributor.advisorDendrinos, Spyridon
dc.contributor.advisorCarroll, Thomas
dc.contributor.authorMeade, Conoren
dc.contributor.funderUniversity College Cork
dc.date.accessioned2025-05-12T10:14:43Z
dc.date.available2025-05-12T10:14:43Z
dc.date.issued2023
dc.date.submitted2023
dc.description.abstractThis 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.en
dc.description.statusNot peer revieweden
dc.description.versionAccepted Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationMeade, C. 2023. Lebesgue space bounds for 2-surfaces in convolution and decoupling. PhD Thesis, University College Cork.
dc.identifier.endpage79
dc.identifier.urihttps://hdl.handle.net/10468/17416
dc.language.isoenen
dc.publisherUniversity College Corken
dc.relation.projectUniversity College Cork (School of Mathematical Sciences, Boole fellowship)
dc.rights© 2023, Conor Meade.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectMathematics
dc.subjectHarmonic analysis
dc.titleLebesgue space bounds for 2-surfaces in convolution and decoupling
dc.typeDoctoral thesisen
dc.type.qualificationlevelDoctoralen
dc.type.qualificationnamePhD - Doctor of Philosophyen
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