Steve Hofmann, 4.1, An Introduction to Harmonic Analysis on Non-Smooth Sets
Channel: IAS | Park City Mathematics Institute | PCMI
Date: 2018-07-06

An Introduction to Harmonic Analysis on Non-Smooth Sets
Steve Hofmann, University of Missouri

Link to lecture notes at:
https://pcmi.ias.edu/sites/pcmi.ias.edu/files/Hofmann_Lecture_Notes.pdf
All lecture notes from PCMI 2018 available at https://pcmi.ias.edu/program-gss/2018ss

This course will be an introduction to harmonic analysis on non-smooth sets, that is, Lipschitz graphs and beyond. The material serves as a starting point for the theory of elliptic equations in domains with rough boundaries. A tentative list of topics to be covered is as follows:
 • T1/Tb theory;
 • Singular integrals on Lipschitz surfaces (Coifman-McIntosh-Meyer Theorem);
 • Square functions;
 • Extension of singular integral and square function theory beyond Lipschitz graphs.
Prerequisites. Theory of measure and integration. Ideally, some familiarity with the basics of harmonic analysis in Euclidean space (e.g., Hardy-Littlewood maximal function, basic Calderón-Zygmund theory).

Presented at the Presented at the 28th Annual PCMI Summer Session will be held July 1–21, 2018, at the Prospector Conference Center in Park City, Utah. The residential, three-week Summer Session is the flagship activity of the IAS/Park City Mathematics Institute (PCMI), an outreach program of the Institute for Advanced Study. The 2018 research theme is Harmonic Analysis.

The PCMI Summer Session is an intensive program that includes several parallel sets of activities aimed at different groups of participants across the entire mathematics community. These activities include a program for mathematics researchers, eight mini-courses for graduate students on topics related to harmonic analysis, two lecture series for undergraduate students, a program for faculty from predominantly undergraduate institutions, a workshop on equity and mathematics education for undergraduate faculty, and a professional development program for K–12 school teachers. All of PCMI’s groups meet simultaneously, pursuing individual courses of study and a meaningful amount of interaction both scientifically and socially.

For more information, visit https://pcmi.ias.edu