  In this paper, we provide necessary and sufficient conditions on a triple of
weights $(u, v, w)$ so that the $t$-Haar multipliers $T^t_{w,\sigma}, t \in
\mathbb{R}$, are uniformly (on the choice of signs $\sigma$) bounded from
$L^2(u)$ into $L^2(v)$. These dyadic operators have symbols $s(x; I) = \sigma_I
(w(x)/\langle w \rangle_I )^t$ which are functions of the space variable $x \in
\mathbb{R}$ and the frequency variable $I \in \mathcal{D}$, making them dyadic
analogues of pseudo-differential operators. Here $\mathcal{D}$ denotes the
dyadic intervals, $\sigma_I = \pm 1$, and $\langle w \rangle_I$ denotes the
integral average of $w$ on $I$. When $w\equiv 1$ we have the martingale
transform and our conditions recover the known two-weight necessary and
sufficient conditions of Nazarov, Treil and Volberg. We also show how these
conditions are simplified when $u = v$. In particular, the martingale
one-weight and the t-Haar multiplier unsigned and unweighted (corresponding to
$\sigma_I= 1$ and $u = v \equiv 1$) known results are recovered or improved. We
also obtain necessary and sufficient testing conditions of Sawyer type for the
two-weight boundedness of a single variable Haar multiplier similar to those
known for the martingale transform.
