Haar Shifts, Commutators, and Hankel Operators

TL;DR

This paper investigates the relationship between Hankel operators, Haar shifts, and commutators, providing a decomposition of the commutator into paraproducts to deepen understanding of their analytic and real-variable interactions.

Contribution

It introduces a novel decomposition of the commutator [H,b] into paraproducts, linking Hankel operators with Haar shifts and commutators in a new analytical framework.

Findings

Decomposition of [H,b] into paraproducts

Enhanced understanding of Hankel operators in analytic and real-variable contexts

Framework connecting Haar shifts with commutator analysis

Abstract

Hankel operators lie at the junction of analytic and real-variables. We will explore this junction, from the point of view of Haar shifts and commutators. An decomposition of the commutator [H,b] into paraproducts is presented.