$Tb$ theorem on product spaces

TL;DR

This paper establishes a $Tb$ theorem for product spaces $R^n imes R^m$, extending harmonic analysis techniques to multi-parameter settings with para-accretive functions.

Contribution

It introduces a $Tb$ theorem on product spaces with para-accretive functions, advancing the understanding of multi-parameter harmonic analysis.

Findings

Proves a $Tb$ theorem on $R^n imes R^m$.

Extends classical $Tb$ theorems to product spaces.

Utilizes para-accretive functions in the theorem's framework.

Abstract

In this paper, we prove a $Tb$ theorem on product spaces $\Bbb R^n\times \Bbb R^m$, where $b(x_1,x_2)=b_1(x_1)b_2(x_2)$, $b_1$ and $b_2$ are para-accretive functions on $\Bbb R^n$ and $\Bbb R^m$, respectively.