Multilinear Dyadic Operators And Their Commutators
Ishwari Kunwar
TL;DR
This paper introduces multilinear dyadic operators and their commutators, explores their boundedness, and characterizes dyadic BMO functions through these properties, advancing the understanding of multilinear harmonic analysis.
Contribution
It develops multilinear analogues of dyadic operators and provides new characterizations of dyadic BMO functions based on operator boundedness.
Findings
Multilinear dyadic paraproducts and Haar multipliers are bounded under certain conditions.
Dyadic BMO functions are characterized via boundedness of specific paraproducts.
Commutators of multilinear Haar multipliers are also bounded, linking to BMO spaces.
Abstract
We introduce multilinear analogues of dyadic paraproduct operators and Haar Multipliers, and study boundedness properties of these operators and their commutators. We also characterize dyadic BMO functions via the boundedness of certain paraproducts and also via the boundedness of the commutators of multilinear Haar Multipliers and paraproduct operators.
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