ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 64, Issue 1, pp 111–144 | Cite as

Multilinear dyadic operators and their commutators

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Abstract

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.

Keywords

Multilinear paraproducts Multilinear Haar multipliers Dyadic BMO functions Commutators 

Mathematics Subject Classification

42A45 42B20 42B25 

Notes

Acknowledgments

The author would like to thank Brett Wick for suggesting him this research project, and for providing valuable suggestions.

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Copyright information

© Università degli Studi di Ferrara 2016

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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