Georgia Institute of Technology College of Sciences

We describe how time-frequency analysis is used to analyze boundedness and Schatten class properties of pseudodifferential operators and Fourier integral operators.

Given an "infinite symmetric matrix" W we give a simple condition, related to the shift operator being expansive on a certain sequence space, under which W is positive. We apply this result to AAK-type theorems for generalized Hankel operators, providing new insights related to previous work by S. Treil and A. Volberg. We also discuss applications and open problems.

We will survey recent developments in the area of two weight inequalities, especially those relevant for singular integrals.  In the second lecture, we will go into some details of recent characterizations of maximal singular integrals of the speaker, Eric Sawyer, and Ignacio Uriate-Tuero.

We will survey recent developments in the area of two weight inequalities, especially those relevant for singular integrals.  In the second lecture, we will go into some details of recent characterizations of maximal singular integrals of the speaker, Eric Sawyer, and Ignacio Uriate-Tuero.