Calder\'{o}n commutators and the Cauchy integral on Lipschitz curves revisited III. Polydisc extensions

TL;DR

This paper extends Calderón commutator and Cauchy integral results to polydiscs, providing new proofs and solving an open problem from the 1980s, advancing the understanding of these operators in higher dimensions.

Contribution

It introduces polydisc extensions of Calderón commutators and Cauchy integrals, completing the series of proofs and resolving a longstanding open question.

Findings

Extended Calderón commutator results to polydiscs

Provided new proofs for classical theorems in higher dimensions

Solved an open problem posed by Coifman in the 1980s

Abstract

This article is the last in a series of three papers, whose scope is to give new proofs to the well known theorems of Calder\'{o}n, Coifman, McIntosh and Meyer. Here we extend the results of the previous two papers to the polydisc setting. In particular, we solve completely an open question of Coifman from the early eighties.