Sparse Domination for Bi-Parameter Operators Using Square Functions

Alexander Barron, Jill Pipher

Let $S$ be the dyadic bi-parameter square function $$Sf(x{)}^2=\sum _{R\in \mathcal{D}}|⟨f,h_R⟩{|}^2\frac{1_R(x)}{|R|}.$$ We prove that if $T$ is a bi-parame…