Analysis Seminar

Square function inequalities and superorthogonality

Lillian Pierce, Duke University

Friday, February 12th, 2021
12:00 PM - 1:00 PM
Zoom ID 573 239 4086

We’ll talk about two notions of square function inequality, related to a sequence of functions, which we’ll call direct and converse inequalities. In many cases the direct inequality can be proved by verifying a type of \(2r\)-superorthogonality, that is, proving that the integral of certain \(2r\)-tuples of functions selected from the sequence vanishes. We will demonstrate a hierarchy of “types” of superorthogonality and we will illustrate how this allows us to unify proofs of classical theorems in a wide variety of settings in harmonic analysis. Moreover, we will show that two famous results from number theory, in the setting of bounding character sums, also fit neatly into this new perspective.

Event contact: dan dot geba at rochester dot edu