MATH 7150 - Fourier Analysis

Camil Muscalu, fall 2016.

The class is an introduction to Euclidean harmonic analysis. Topics usually include convergence of Fourier series, harmonic functions and their conjugates, Hilbert transform, Calderón-Zygmund theory, Littlewood-Paley theory, duality between the Hardy space $H^1$ and $BMO$, paraproducts, Fourier Restriction and applications, etc. If time permits, applications to PDE and number theory will also be discussed.

Textbook

C. Muscalu and W. Schlag, Classical and multilinear harmonic analysis, Vol 1 and 2, Cambridge Studies in Advanced Mathematics, Cambridge University Press, 2013.