Lectures: MWF 2:00PM-2:50PM at Thack 704
Office hours: By appointment, held at Thackeray Hall 610.
Content and Prerequisites:
This course is an introduction to Harmonic Analysis.
Textbook: There is no required textbook. The following resources are recommended:
E.M. Stein, Singular integrals and differentiability properties of functions.
E.M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals.
E.M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces.
L. Grafakos, Modern Fourier analysis.
L. Grafakos, Classical Fourier analysis.
J. Duoandikoetxea, Fourier analysis.
A tentative syllabus:
The course is a continuation of Analysis 1,2 and 3 and it will be an introduction to classical harmonic analysis on the Euclidean spaces. Topics include: maximal functions, Riesz potentials, singular integrals, Fourier transform, tempered distributions, Hilbert transform, Riesz transforms, Calderon-Zygmund operators, interpolation, Marcinkewicz and Hormander multiplier theorems, Littlewood-Paley theory, Hardy space and BMO, Stein spherical maximal theorem, Muckenhoupt weights, Bessel potentials.
Grading: Homework (20%), Take home midterm (40%), Take home final exam (40%).
Homework: There will be a limited number of homeworks which will appear on this website and will be collected on Mondays in class. They will NOT be returned to you so make a copy for yourself before handing in your homework.
Midterm and final exam: They will be take home and will be announced in advance.