Math 545
Harmonic Analysis


Spring 2020 Course Information


Instructor Xiaochun Li
Office 342 Illini Hall
Lectures MWF 9:00-9:50 in 2 Illini Hall
Office Hours MW 9:50-10:50.
TA TBA
Textbook No textbook
References Javier Douandikoetxea, Fourier analysis, Graduate studies in math. Vol. 29., AMS, 2001.
E. M. Stein, Singular integrals and differentiablity properties of functions, Princeton Univ. Press, Princeton, 1970.
E. M. Stein, Harmonic analysis: Real variable methods, Princeton Univ. Press, Princeton, 1993.
E. M. Stein and G. Weiss, Introduction to Fourier Analysis in Euclidean Spaces, Princeton Univ. Press, Princeton, 1971.
T. H. Wolff, Lectures on Harmonic Analysis, Univ. Lecture Series, Vol. 29, AMS, 2003
Exams No exams!
Grading Homework: 100%
Students need to turn in ALL homework assigned in class in the end of semester.
Syllabus The following topics are planed to be covered.
  • Marcinkiewicz interpolation; Approximation to the identity; Fourier transforms;
  • The theory of Calderon-Zygmund singular integrals;
  • Littlewood-Paley theory; Multiplies;
  • BMO and Carleson measure; T1 theroem;
  • Besicovitch sets and the unboundedness of the disk multiplier;
  • Oscillatory integrals
Prerequisites Solid knowledge of real analysis.