A local $Tb$ theorem for square functions in domains with Ahlfors-David regular boundaries

TL;DR

This paper establishes a local Tb theorem for square functions in domains with Ahlfors-David regular boundaries, extending previous work to broader geometric settings with L^p control of pseudo-accretive systems.

Contribution

It extends the local Tb theorem for square functions to domains with Ahlfors-David regular boundaries under L^p control, broadening the scope of prior results.

Findings

Proves a local Tb theorem for square functions in new geometric settings

Extends Hofmann's work to Ahlfors-David regular domains

Provides L^p control conditions for pseudo-accretive systems

Abstract

We prove a local Tb Theorem for square functions, in which we assume L^p control of the pseudo-accretive system, with p>1 extending the work of S. Hofmann to domains with Ahlfors-David regular boundaries.