Dyadic representation and boundedness of non-homogeneous   Calder\'on--Zygmund operators with mild kernel regularity
  We prove a new dyadic representation theorem with applications to the $T(1)$ and $A_2$ theorems. In particular, we obtain the non-homogeneous $T(1)$ theorem under weaker kernel regularity than the earlier approaches. 
Ana Grau de la Herr\'an and Tuomas Hyt\"onen
math.FA