We state our results before providing a broader context.

Call a collection of cubes $ \mathcal S  $ in $ \mathbb R ^{n}$ a *sparse* collection if there is a set $ E_Q \subset Q$ for each $ Q\in \mathcal S$ so that (a) $ \lvert  E_Q\rvert >c \lvert  Q\rvert $ for each $ Q\in \mathcal S$, and (b) the collection of sets $\{ E_Q \;:\; Q\in \mathcal S\}$ are pairwise disjoint. Here $ 0< c< 1$ will be a dimensional constant that we do not track. Define a *sparse bilinear form* to be $$\label{e:sparseOp}
\Lambda _{r,s} (f,g) = \sum_{Q\in \mathcal S}  \langle f \rangle _{Q,r} \langle g \rangle _{Q,s} \lvert  Q\rvert,   \qquad 1 \leq  r, s < \infty .$$ Above, $ \langle  f \rangle _{Q,r} ^{r}  :=   \lvert 3 Q\rvert ^{-1} \int _{3Q} \lvert  f\rvert ^{r}    \;dx $, and if $ r=s$, then $ \Lambda _{r} = \Lambda _{r,r}$. We frequently suppress the collection of sparse cubes $ \mathcal S$.

We consider Calderón-Zygmund singular integral operators $ T $, defined to be an $ L ^2 (\mathbb R ^{n})$ bounded convolution operator given by $$\langle T f, g \rangle = \int\!\int K (x-y) f (y) g (x) \; dx\,dy 