MATH 711: Fourier Analysis II (Fall 2005)

Instructor: Camil Muscalu

Meeting Time & Room

This is a continuation of our "Fourier Analysis I" course given in Spring 2005.

The plan is to cover the following topics:

  1. Real variable theory of Hardy spaces, atomic decomposition
  2. BMO, Carleson measures, John-Nirenberg inequality
  3. C.Fefferman's duality between H^1 and BMO
  4. T1 theorem of David and Journe
  5. Calderon's commutators
  6. L^2 boundedness of the Cauchy integral on Lipschitz curves
  7. Weighted inequalities
  8. Pseudo-differential operators
  9. Oscillatory integrals, the methods of stationary and nonstationary phase
  10. Heisenberg uncertainty principle, Bernstein inequality, Sobolev embedding theorem
  11. Besicovitch sets and C.Fefferman's counterexample for the ball multiplier
  12. Bochner-Riesz, Kakeya and Restriction theorems in two dimensions

We shall use various sources, but mostly the classical books of Michael Christ and Elias Stein:

  • M. Christ — Lectures on singular integrals operators, CBMS Series 77 [1990].
  • E. Stein — Harmonic analysis: real-variable methods, orthogonality and oscillatory integrals, Princeton Univ. Press [1993].

Last modified: April 5, 2005