05/06/2026
We are pleased to announce that Troy Roberts from Washington University St. Louis and former UA student will be giving a Analysis Seminar talk today at 11:00 AM in GP 346 . Please see below for title and abstract.
Title: Testing Theorems and Matrix Weights
Abstract: To show that an operator T from X to Y is bounded, one typically must compute the norm of Tx for all unit vectors x in X. Testing theorems tell you that in certain cases it is enough to compute the norm of Tx for all vectors in a "nice" subclass of X. This approach proved very useful in studying the two-weight problem, i.e., when operators are bounded from L^p(w) to L^p(v) for two different weights w and v.
We will discuss results of this type with particular emphasis on the well-localized operators introduced by Nazarov, Treil, and Volberg. We will also talk about our efforts to generalize these results to the matrix weight setting when p is not 2 and discuss some of the difficulties that arise.