A Bellman function proof of the $L^2$ bump conjecture
  We approach the problem of finding the sharp sufficient condition of the boundedness of all two weight Calderon--Zygmund operators. We solve this problem in $L^2$ by writing a formula for a Bellman function of the problem. 
Fedor Nazarov, Alexander Reznikov, Sergei Treil, Alexander Volberg
math.CA math.AP