Multilinear dyadic operators and their commutators
Kunwar, Ishwari J.
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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.