A local $Tb$ theorem for square functions in domains with Ahlfors-David   regular boundaries
  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. 
Ana Grau de la Herran, Mihalis Mourgoglou
math.CA