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dc.contributor.advisorGrafakos, Loukaseng
dc.contributor.authorNguyen, Hanh Van (Researcher on mathematics)eng
dc.date.issued2016eng
dc.date.submitted2016 Summereng
dc.descriptionAbstract from public.pdf file.eng
dc.descriptionDissertation supervisor: Dr. Loukas Grafakos.eng
dc.descriptionIncludes vita.eng
dc.description.abstractThe first topic of this dissertation is concerned with the L^2 boundedness of a maximal Fourier integral operator which arises by transferring the spherical maximal operator on the sphere S^n to a Euclidean space of the same dimension. Thus, we obtain a new proof of the boundedness of the spherical maximal function on S^n. In the second part, we obtain boundedness for m-linear multiplier operators from a product of Lebesgue (or Hardy spaces) on R^n to a Lebesgue space on R^n, with indices ranging from zero to infinity. The multipliers lie in an L^2-based Sobolev space on R^{mn} uniformly over all annuli, just as in Hörmander's classical multiplier condition. Moreover, via proofs or counterexamples, we find the optimal range of indices for which the boundedness holds within this class of multilinear Fourier multipliers.eng
dc.description.bibrefIncludes bibliographical references (pages 96-98).eng
dc.format.extent1 online resource (v, 99 pages) : illustrationseng
dc.identifier.merlinb11890081xeng
dc.identifier.oclc991527827eng
dc.identifier.urihttps://hdl.handle.net/10355/57249
dc.identifier.urihttps://doi.org/10.32469/10355/57249eng
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcommunityUniversity of Missouri--Columbia. Graduate School. Theses and Dissertationseng
dc.rightsOpenAccess.eng
dc.rights.licenseThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.eng
dc.subject.FASTFourier integral operatorseng
dc.titleMaximal Fourier integrals and multilinear multiplier operatorseng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelDoctoraleng
thesis.degree.namePh. D.eng


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