Vector-valued inequalities with applications to bi-parameter problems.

Analysis Seminar
Wednesday, March 12, 2014 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Prabath Silva – Indiana University
Brett Wick
In this talk we will discuss applications of a new method of proving vector-valued inequalities discovered by M. Bateman and C. Thiele. We give new proofs of the Fefferman-Stein inequality (without using weighted theory) and vector-valued estimates of the Carleson operator using this method. Also as an application to bi-parameter problems, we give a new proof for bi-parameter multipliers without using product theory. As an application to the bilinear setting, we talk about new vector-valued estimates for the bilinear Hilbert transform, and estimates for the paraproduct tensored with the bilinear Hilbert transform. The first part of this work is joint work with Ciprian Demeter.