COMPARISON OF T1 CONDITIONS FOR MULTI-PARAMETER OPERATORS.

When Journé established the classical multi-parameter singular integral theory in 1985, it was formulated in the language of vector-valued Calderón-Zygmund theory. In 2011, Pott and Villarroya formulated a new T1 Theorem for product spaces. In their work, they replaced the vectorvalued formulations for several mixed type conditions. Inspired by their work, Martikainen redefined the bi-parameter operators. Originally, it was thought that this new class of operators was larger (and contained the ones defined by Journé). In this paper we prove that both classes are actually equal. [ABSTRACT FROM AUTHOR]