Harmonic analysis 1000-1M10AH

1. Introduction. L1(T) algebra. Fourier coefficients.
2. The Riemann-Lebesgue lemma. Approximative kernels.
3. Convergence of Fejer and Poisson means almost everywhere.
4. Order of magnitude of Fourier coefficients.
5. Fourier series of square summable functions.
6. Algebra of absolutely summing Fourier series.
7. Pointwise convergence of Fourier series (Dini and Lipschitz criteria).
8. Sets of divergence.
9. Hardy's spaces. Conjugate function.
10. Hilbert's inequality. Theorem of Hardy and Littlewood. Theorem of
F. and M. Riesz.
11. Theorems of Kolmogorov and Zygmund. Riesz and Hilbert transform.
12. Calderon-Zygmund theory.
13. Introduction to multipliers. Hormander-Michlin theorem.
14. McGehee-Pigno-Smith theorem (Littlewood conjecture proved also by
Konyagin).
15. Basic information about Fourier-Stieltjes coefficients of measure.
16. Idempotent measures and Helson's theorem.