Multilinear dyadic operators and their commutators
We obtain a generalized paraproduct decomposition of the pointwise product of two or more functions that naturally gives rise to multilinear dyadic paraproducts and Haar multipliers. We then study the boundedness properties of these multilinear operators and their commutators with dyadic BMO functions. We also characterize the dyadic BMO functions via the boundedness of (a) certain paraproducts, and (b) the commutators of multilinear Haar multipliers and paraproduct operators.
KeywordsMultilinear paraproducts Multilinear Haar multipliers Dyadic BMO functions Commutators
Mathematics Subject Classification42A45 42B20 42B25
The author would like to thank Brett Wick for suggesting him this research project, and for providing valuable suggestions.
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