Perfect dyadic operators: Weighted T(1) theorem and two weight estimates

Perfect dyadic operators were first introduced in [1], where a local T(b)T(b) theorem was proved for such operators. In [3] it was shown that for every singular integral operator T   with locally bounded kernel on Rn×RnRn×Rn there exists a perfect dyadic operator TT such that T−TT−T is bounded on Lp(dx)Lp(dx) for all 1