The Two Weight Inequality for the Hilbert Transform

Research Horizons Seminar
Wednesday, February 13, 2013 - 12:05
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech, School of Math
I'll introduce the Hilbert transform in a natural way justifying it as a canonical operation.  In fact, it is such a basic operation, that it arises naturally in a range of settings, with the important complication that the measure spaces need not be Lebesge, but rather a pair of potentially exotic measures.  Does the Hilbert transform map L^2 of one measure into L^2 of the other?  The full characterization has only just been found.  I'll illustrate the difficulties with a charming example using uniform measure on the standard 1/3 Cantor set.