Fall 2025
Sagun Chanillo
Course Description:
Topics:
1. Interpolation theorems in generality of Marcinkiewicz, Riesz-Thorin and Stein.
2. Riesz potentials, Hardy-Littlewood-Sobolev fractional integration theorem. Poincare
and local Sobolev inequalities. Gagliardo-Nirenberg theorem, Moser-Trudinger inequality.
3. Calderon-Zygmund singular integrals the L
2
theory. The non-convolution case Cotlar’s
Lemma.
4. The L
p
theory of singular integrals, the Calderon-Zygmund decomposition.
5. Maximal singular integrals.
6. BMO, the Spanne-Stein theorem, the John-Nirenberg inequality.
7. The Fefferman-Stein sharp function.
8. H¨ormander’s multiplier theorem.
9. Khinchine’s inequality/ large deviation estimate and the Littlewood-Paley theorem.
10. Restriction theory of the Fourier transform.
11. Bochner-Riesz theorem of Fefferman and Strichartz inequality.
12. The theory of Ap weights and Muckenhoupt’s theory for the Hardy-Littlewood maximal
function and weighted inequalities for singular integrals.
13. (Time permitting) Carleson measures and Fefferman’s theorem that BMO is the dual
of Hardy space.
Text:
There is no textbook for this course. Lecture notes for each Lecture will be
posted on Canvas.
Prerequisites:
501 and 503
Schedule of Sections:
16:640:521 Schedule of Classes
Previous Semesters:
- Fall 2025 - Chanillo, Sagun
- Fall 2023 - Chanillo, Sagun
- Fall 2022 - Mirek, Mariusz
- Fall 2020 Prof. Chanillo