Multilinear dyadic operators and their commutators

Multilinear dyadic operators;Paraproducts;Haar multipliers;Commutators;Dyadic BMO functions;Multilinear sparse operators;Multilinear Bloom's inequality

Kunwar, Ishwari J. ; Lacey, Michael T. Wick, Brett D. Mathematics Heil, Christopher Lubinsky, Doron Nitzan, Shahaf ; Lacey, Michael T.

University:Georgia Institute of Technology

Department:Mathematics

关键词: Multilinear dyadic operators;    Paraproducts;    Haar multipliers;    Commutators;    Dyadic BMO functions;    Multilinear sparse operators;    Multilinear Bloom's inequality;   

Others  :  https://smartech.gatech.edu/bitstream/1853/58717/1/KUNWAR-DISSERTATION-2017.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

In this dissertation, we present a systematic study of multilinear dyadic operators and their commutators with locally integrable functions. We obtain a generalized paraproduct decomposition of the pointwise product of two or more functions, which naturally gives rise to multilinear dyadic paraproducts and Haar multipliers. We study boundedness properties of these operators and their commutators in various settings. Moreover, we show that these multilinear dyadic operators and their commutators can be pointwise dominated by multilinear sparse operators. We also introduce multilinear Bloom’s inequality and prove it for the commutators of multilinear Haar multipliers with dyadic BMO functions. Along the way, we obtain several characterizations of dyadic BMO functions.