dc.contributor.advisor Torres, Rodolfo H dc.contributor.author Chaffee, Lucas dc.date.accessioned 2015-12-02T23:53:37Z dc.date.available 2015-12-02T23:53:37Z dc.date.issued 2015-05-31 dc.date.submitted 2015 dc.identifier.other http://dissertations.umi.com/ku:14038 dc.identifier.uri http://hdl.handle.net/1808/19020 dc.description.abstract In this dissertation we further develop the theory of commutators of multilinear singular integral operators with pointwise multiplication. Generally speaking, the commutator of two operators is itself an operator that measures the changes which occur when switching the order in which the commuted operators are being applied. They have proven to be significant historically, and can be useful in the study of PDE. Our first main contribution is the completion of the characterization of the space functions with bounded mean oscillation (BMO) in terms of the boundedness of the corresponding commutator in an appropriate set of Lebesgue spaces. It is already known in a variety of settings that a function being in BMO is sufficient to conclude the boundedness of the commutator, we were able to show that this condition is in fact necessary, a long standing open question. Our characterization opened the door for us to obtain our second main result, namely the necessary and sufficient conditions which guarantee the compactness of the commutator of the bilinear singular integral with pointwise multiplication in appropriate weighted Lebesugue spaces. dc.format.extent 58 pages dc.language.iso en dc.publisher University of Kansas dc.rights Copyright held by the author. dc.subject Mathematics dc.subject BMO dc.subject Calderon Zygmund Theory dc.subject Commutators dc.subject Harmonic Analysis dc.subject Multilinear Operators dc.subject Singular integrals dc.title Commutators of Multilinear Singular Integral Operators with Pointwise Multiplication dc.type Dissertation dc.contributor.cmtemember Gavosto, Estela dc.contributor.cmtemember Orr, Jim dc.contributor.cmtemember Shao, Shuanglin dc.contributor.cmtemember Stefanov, Atanas dc.thesis.degreeDiscipline Mathematics dc.thesis.degreeLevel Ph.D. dc.rights.accessrights openAccess
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