Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds   for the q-variation of singular integrals
  Any Calderon-Zygmund operator T is pointwise dominated by a convergent sum of positive dyadic operators. We give an elementary self-contained proof of this fact, which is simpler than the probabilistic arguments used for all previous results in this direction. Our argument also applies to the q-variation of certain Calderon-Zygmund operators, a stronger nonlinearity than the maximal truncations. As an application, we obtain new sharp weighted inequalities. 
Tuomas P. Hyt\"onen and Michael T. Lacey and Carlos P\'erez
math.CA