Math 247A (Harmonic Analysis).
Lectures: MWF 9:00am-9:50am in MS 5148.
Instructor: Monica Visan, MS 6167. Email address: visan@math.ucla.edu
Office Hours: Wed 1:00pm-2:00pm.
Topics:
- Basic properties of the Fourier transform in Rd.
- Maximal and vector maximal inequalities.
- Calderon-Zygmund singular integral operators.
- Littlewood-Paley theory.
- Fractional chain/product rules.
- Stationary phase.
- Rearrangement inequalities.
References:
- E. Stein, Harmonic analysis: real-variable methods,
orthogonality, and oscillatory integrals. Princeton Mathematical
Series, 43. Princeton University Press, 1993.
- E. Stein, Singular integrals and differentiability properties of
functions. Princeton Mathematical Series, 30. Princeton University
Press, 1970.
Grading: Grading will be based solely on the homework. Problems
will be assigned and collected throughout the quarter.
Homework: You may collaborate on the homework, but solutions need
to be written up in your own words.