The A_2 Theorem for spaces of homogeneous type

Analysis Seminar
Wednesday, February 27, 2013 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Theresa Anderson – Brown University
Michael Lacey
A recent conjecture in harmonic analysis that was exploredin the past 20 years was the A_2 conjecture, that is the sharp bound onthe A_p weight characteristic of a Calderon-Zygmund singular integraloperator on weighted L_p space. The non-sharp bound had been knownsince the 1970's, but interest in the sharpness was spurred recentlyby connections to quasiconformal mappings and PDE. Finally solved infull by Hytonen, the proof is complex, intricate and lengthy. A new "simple" approach using local mean oscillation and positive operatorbounds was published by Lerner. We discuss this and some recent progress in the area, including our new proof for spaces of homogeneoustype, in the style of Lerner (Joint work with Armen Vagharshakyan).