Weighted Inequalities for Singular Integral Operators

Weighted norm inequalities for singular integrals have received much attention in recent years. Via local mean oscillation, Andrei Lerner was able to bound Calderon-Zygmund operators in norm by positive dyadic operators. I will focus on how the innovative techniques of Lerner, that I have worked to extend, have led to new results in the area of sharp weighted norm inequalities (and beyond if time allows).