Composition of Haar Paraproducts: The Random Case
Dmitriy Bilyk, Michael Lacey, Xiaochun Li, Brett Wick
TL;DR
This paper investigates the boundedness of compositions of Haar paraproducts, focusing on randomized variants to uncover new characterizations relevant to harmonic analysis and operator theory.
Contribution
It introduces non-classical characterizations for the boundedness of dyadic paraproduct compositions in the context of randomized variants.
Findings
Identifies conditions under which randomized Haar paraproduct compositions are bounded.
Establishes connections to the two-weight problem for the Hilbert transform.
Provides new insights into the composition of Hankel matrices and related operators.
Abstract
When is the composition of paraproducts bounded? This is an important, and difficult question, related to to a question of Sarason on composition of Hankel matrices, and the two-weight problem for the Hilbert transform. We consider randomized variants of this question, finding non-classical characterizations, for dyadic paraproducts.
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