A simple proof of the $A_2$ conjecture
The $A_2$ conjecture says that the $L^2(w)$ operator norm
of any Calder\'on-Zygmund operator is bounded linearly by the $A_2$
constant of the weight $w$.
This conjecture was completely solved in 2010 by T. Hyt\"onen.
The proof was based on a rather difficult representation of a general
Calder\'on-Zygmund operator in terms of the Haar shift operators.
In this talk we shall discuss a recent simpler proof completely
avoiding the notion of the Haar shift operator.