Analysis Seminar: Weighted Inequalities and the Testing Philosophy in Harmonic Analysis
Speaker: Troy Roberts, Washington University in St. Louis
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.
Note: This talk is given in partial fulfillment of the Third Year Candidacy Requirement.