  Let M denote the dyadic Maximal Function. We show that there is a weight w,
and Haar multiplier T for which the following weak-type inequality fails: $$
\sup_{t>0}t w\left\{x\in\mathbb R \mid |Tf(x)|>t\right\}\le C \int_{\mathbb
R}|f|Mw(x)dx. $$ (With T replaced by M, this is a well-known fact.) This shows
that a dyadic version of the so-called Muckenhoupt-Wheeden Conjecture is false.
This accomplished by using current techniques in weighted inequalities to show
that a particular $L^2$ consequence of the inequality above does not hold.
