Localization and Toeplitz operators with complex Borel measure symbols on weighted Bergman spaces

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dc.contributor.authorSadeghi, Mohammad
dc.contributor.examiningcommitteeClouatre, Raphael (Mathematics) Martin, Robert (Mathematics) Wick, Brett (Washington Universityen_US
dc.contributor.supervisorZorboska, Nina (Mathematics)en_US
dc.date.accessioned2021-06-10T16:53:02Z
dc.date.available2021-06-10T16:53:02Z
dc.date.copyright2021-06-10
dc.date.issued2021-05-28en_US
dc.date.submitted2021-06-01T22:39:54Zen_US
dc.date.submitted2021-06-10T15:07:11Zen_US
dc.degree.disciplineMathematicsen_US
dc.degree.levelDoctor of Philosophy (Ph.D.)en_US
dc.description.abstractWe extend the definition of weak localization to the weighted Bergman spaces of the unit ball, L^2_a(B_n, dV_alpha), for alpha>-1. We prove that a Toeplitz operator with a complex Borel measure symbol whose total variation is Carleson is weakly localized on L^2_a(B_n, dV_alpha). We extend the definitions of strongly localized and sufficiently localized operators defined in the paper of the Ph.D. candidate and Prof. N. Zorboska, to the weighted Bergman spaces L^2_a(B_n, dV_alpha) and show that they are also weakly localized. We also show that bounded Toeplitz operators with BMO^1 symbols are strongly (and therefore also weakly) localized. Finally, we prove that the Toeplitz operators induced by the complex Borel measures with Carleson total variation are weakly localized on the spaces L^2_a(omega) with the weight omega in class E.en_US
dc.description.noteOctober 2021en_US
dc.identifier.citationLocalization, Carleson measure, and BMO Toeplitz operators on the Bergman space, with Nina Zorboska, J. Math. Anal. Appl. 485 (2020),123829en_US
dc.identifier.urihttp://hdl.handle.net/1993/35695
dc.language.isoengen_US
dc.rightsopen accessen_US
dc.subjectLocalizationen_US
dc.subjectToeplitz Operatorsen_US
dc.subjectComplex Measuresen_US
dc.subjectCarleson Measuresen_US
dc.subjectWeighted Bergman Spacesen_US
dc.titleLocalization and Toeplitz operators with complex Borel measure symbols on weighted Bergman spacesen_US
dc.typedoctoral thesisen_US
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