PDE/Applied Seminar: Francisco Villarroya (University of Lund, Sweden), 'Compact T(1) Theory'

Event Date: 

Friday, April 26, 2013 -
3:00pm to 4:00pm

Event Location: 

  • 4607B South Hall

Event Contact: 

Carlos Garcia-Cervera

Email: cgarcia@math.ucsb.edu

We prove a T(1)-type theorem which characterizes compactness of singular integral operators whose kernels satisfy a smoothness condition with decay along the diagonal.

In the same spirit of David and Journe's original T(1) Theorem, we provide this characterization in terms of the action of the operator over special families of functions. For this reason, we define a new property of 'weak compactness' and the appropriate substitute for the space BMO.

We apply our main theorem to prove compactness of certain perturbations of the Cauchy Integral.