Characterization of matrix valued BMO by commutators and sparse domination of operators

BMO;Commutators;Sparse operators;Sparse;Sparse forms

Mena Arias, Dario Alberto ; Lacey, Michael T. Heil, Christopher Iliev, Plamen Nitzan, Shahaf Wick, Brett Mathematics ; Lacey, Michael T.

University:Georgia Institute of Technology

Department:Mathematics

关键词: BMO;    Commutators;    Sparse operators;    Sparse;    Sparse forms;   

Others  :  https://smartech.gatech.edu/bitstream/1853/59857/1/MENAARIAS-DISSERTATION-2018.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

In the first part of this thesis, we characterize the space of matrix-valued, two-parameters BMO functions by using commutators with the Hilbert transform. The second part deals with domination of certain operators, by using a class of positive forms which have better boundedness properties and are highly localized. We present a sparse version of the T1 Theorem of David and Journé, the sparse control of a discrete version of the Hilbert transform with an oscillatory term with a quadratic phase, and the sparse domination of the Bochner-Riesz multipliers.