- Course description: Continuation of 245B. Interpolation theory, Fourier analysis, Sobolev spaces, distribution theory. Hausdorff dimension may be covered if time permits.

- This class will be a direct continuation of 245B. A passing grade in 245B (or equivalent) will be a mandatory prerequisite for enrollment in this class.
- The first class is on Monday, March 28. We will begin with 245B Notes 12: Continuous functions on locally compact Hausdorff spaces, and then go through the 245C notes as time permits.
- (Mar 30) Beginning with the next class (i.e. Friday April 1), the class will be held at MS 5128 rather than MS 6229.
- (Apr 19) A second office hour has been set aside at Tu 11-12 (since some students were not able to make the W 1-2 office hour).
- (Apr 22) Due to the second distinguished lecture of Ehud Hrushovski, there will be NO CLASS on Wednesday, Apr 27.

- Instructor: Terence Tao, tao@math.ucla.edu, x64844, MS 6183
- Lecture: MWF 2-2:50, MS 5128 (note change of room)
- Quiz section: N/A
- Office Hours: Tu 11-12; W 1-2
- TA: N/A
- TA Office hours: N/A
- Textbook: Folland's "Real analysis", and my “An epsilon of room, Vol. I.”, available at http://terrytao.wordpress.com/books/an-epsilon-of-room-pages-from-year-three-of-a-mathematical-blog/.
- Prerequisites: A passing grade in 245B (or equivalent) is a mandatory prerequisite for this course. (This course will be a direct continuation of the winter quarter 245B course.)
- Grading: Grading will be based on homework and attendance.
- Reading Assignment: We will cover most of Chapters 1.10-1.15 of “An epsilon of room, Vol. I”.
- Homework: Approximately four homework assignments will be given, mostly from “An epsilon of room, Vol. I”.

- First homework assignment (due Monday, Apr 11):

- Exercise 1.10.9 (Tietze extension theorem for unbounded functions).
- Exercise 1.10.17 (M(X) as dual of C_c(X) and C_0(X)). Note that in this section, X is always assumed to be LCH and sigma-compact.
- Exercise 1.10.25 (Density of Fourier series). Note an important typo in this question: [R,Z] (or [0,1]) should be R/Z (i.e. the unit circle).

- Second homework assignment (due Monday, Apr 25)

- Exercise 1.11.4 (Phragmen-Lindehof principle)
- Exercise 1.11.8 (Weak and strong L^p equivalent up to logarithmic factors). Important typo: log(1+|X|) should be log1/p(1+|X|).
- Exercise 1.11.14 (L^p characterisation of exponential integrability)

- Third homework assignment (due Monday, May 9):

- Exercise 1.11.11 (Characterisation of weak L^p)
- Exercise 1.12.6 (Existence of Haar measure, compact case). You may use Tychonoff’s theorem (Theorem 1.8.14) without proof.
- Exercise 1.12.16 (Pontryagin dual of compact group is discrete)

- Fourth homework assignment (due Monday, May 23):

- Exercise 1.12.20 (Convergence of Fourier series)
- Exercise 1.12.41 (Poisson summation formula)
- Exercise 1.13.16 (Division by x)

- Exams: There is no examination for this course.