A simple proof of the $A_2$ conjecture
  We give a simple proof of the $A_2$ conjecture proved recently by T. Hyt\"onen. Our proof avoids completely the notion of the Haar shift operator, and it is based only on the "local mean oscillation decomposition". Also our proof yields a simple proof of the "two-weight conjecture" as well. 
Andrei K. Lerner
math.CA math.FA