Mathematics Colloquium: Weights in Harmonic Analysis: A Panoramic Exploration of Weighted Inequalities in Various Settings

Speaker:  Nathan Wagner, GMU

Title: Weights in Harmonic Analysis: A Panoramic Exploration of Weighted Inequalities in Various Settings

Abstract:    In this talk, we will explore weighted inequalities, which measure how various integral operators affect the “size” of functions, where the norm or precise notion of “size” depends on the underlying weight. In particular, the norm of a function f and its image under the operator, Tf , are both computed by taking a pth-power integral of the respective function against some positive weight w.  We will begin with some motivation for studying singular integral operators, specifically the Hilbert transform and its weighted theory, by recalling basic harmonic analysis objects such as the Fourier transform and Fourier series. We will then look at such weighted inequalities in a different context motivated by analytic functions of several complex variables. Specifically, I will discuss some of my research activity pertaining to weighted estimates for the Bergman and Cauchy-Szego projections, which are orthogonal projections onto Hilbert spaces of holomorphic functions. Finally, I will illustrate how similar ideas can be applied to study certain discrete operators which serve as useful models for continuous operators such as the Hilbert transform. I will also highlight some open questions related to these topics which may be suitable for graduate students.  

Time:  Friday, October 10, 3:30pm – 4:20pm

Place:  Exploratory Hall, room 4106

Zoom and In-person