## ANNOUNCEMENTS

Registration for Spring term opens Thursday, February 23, 2016.

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## COURSE DESCRIPTION

This is the third quarter of the Graduate Analysis Qualifying Exam course. We will principally cover elementary classical harmonic analysis

## INSTRUCTORS

Nets Katz

International Business Machines Professor of Mathematics

164 Sloan

626-395-2326

## POLICIES

### Grades

Grading based on homeworks, not exams

### Homework Policy

There will be roughly 6 problem sets, no more often than weekly but occasionally less often.

## TOPICS COVERED

This course will cover elementary Fourier series and their convergence, singular integrals, in particular the maximal function and the Hilbert transform, Littlewood Paley theory, Sobolev spaces and the Sobolev embedding theorems, applications to PDE, introduction to radial Fourier multipliers and the Kakeya problem.

## TEXTBOOKS

Analisis de Fourier, Javier Duoandikoetxea Zuazo.Ediciones de la Universidad Autonoma de Madrid [The bookstore is carrying a somewhat disreputable translation, published by the AMS

We will also be using these lecture notes of Terry Tao on Littlewood-Paley theory from which he gave a course in Winter 2001

Here is Lacey and Thiele's paper on Carleson's theorem. Carleson

## HOMEWORK

Due Date | Homework | Solutions |
---|---|---|

April 14, 2017 | Problem set 1 | |

April 28, 2017 | Problem set 2 | |

May 12,2017 | Problem set 3 | |

May 29,2017 | Problem set 4 | |