There will not be a class on Friday March 16.  Have a good spring break!

• The description of this course.
• Week 1 notes: Review of Fourier transform; phase space; uncertainty principle (postscript)  (Corrected Jan 10! Further correction (Apr 2 2021, from Jacob Denson): In the conclusion of Proposition 5.5, all the appearances of I and J should be swapped.)
• Week 2/3 notes: Littlewood-Paley theory; Sobolev spaces (postscript)  (Corrected Feb 20, 2003, thanks to Mark Keel). A further correction (Mar 10, 2010, from Veronica Quitalo): On page 5, the inequality 1/p - 1/q > 1/n should be 1/p-1/q < 1/n. Yet another correction (Mar 16, 2012, from Nefton Pali): in the proof of Lemma 1.1 on page 3, one should replace phi with a function like psi (basically, one needs to smoothly truncate phi near the origin to avoid unnecessary frequency divergences for the second part of the lemma).
• Week 4 notes: Product estimates, multilinear estimates (postscript)
• Week 5 notes: Regularity of harmonic maps (postscript)
• Week 6/7/8 notes: Walsh wave packets, Walsh Carleson theorem (postscript) (Corrected Nov 26, thanks to Dmitry Ryabogin)
• Week 8/9 notes: Haar basis, the Cauchy integral (postscript)
• Week 10 notes: The Lewy example (postscript)

ERRATA for Homework 2:

• Question 1:  W^{p,s} should be W^{s,p}.  Similarly for W^{p,s-sigma}.
• Question 2: The condition 1/q = 1/p + \theta/n should be 1/p = 1/q + \theta/n.
• Question 4(b): The right-hand side should contain a ||f||_p as well as ||\nabla f||_p.

ERRATA for Homework 4:

• Question 1: One should have 0 < s < 1 rather than just s>0.

• Question 1: One should ignore sets of measure zero in this question (and indeed, in all questions in this course).

Back to my home page.