**CBMS Regional Conference Series in Mathematics**

Volume: 105;
2006;
86 pp;
Softcover

MSC: Primary 42;
Secondary 47

Print ISBN: 978-0-8218-3661-3

Product Code: CBMS/105

List Price: $32.00

Individual Price: $25.60

**Electronic ISBN: 978-1-4704-2465-7
Product Code: CBMS/105.E**

List Price: $32.00

Individual Price: $25.60

#### Supplemental Materials

# Wave Packet Analysis

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*Christoph Thiele*

A co-publication of the AMS and CBMS

The concept of “wave packet analysis”
originates in Carleson's famous proof of almost everywhere convergence of
Fourier series of \(L^2\) functions. It was later used by Lacey and
Thiele to prove bounds on the bilinear Hilbert transform. For quite some time,
Carleson's wave packet analysis was thought to be an important idea, but that
it had limited applications. But in recent years, it has become clear that
this is an important tool for a number of other applications. This book is an
introduction to these tools. It emphasizes the classical successes (Carleson's
theorem and the Hilbert transform) in the main development. However, the book
closes with a dedicated chapter on more recent results.

Carleson's original theorem is sometimes cited as one of the most
important developments of 20th century harmonic analysis. The set of
ideas stemming from his proof is now seen as an essential element in
modern harmonic analysis. Indeed, Thiele won the Salem prize jointly
with Michael Lacey for work in this area.

The book gives a nice survey of important material, such as an overview of
the theory of singular integrals and wave packet analysis itself. There is a
separate chapter on “further developments”, which gives a broader
view on the subject, though it does not exhaust all ongoing
developments.

A co-publication of the AMS and CBMS.

#### Readership

Graduate students and research mathematicians interested in classical analysis and harmonic analysis.

#### Reviews & Endorsements

This book is a nice survey of the theory and results that earlier could be found only in various papers. Moreover, it gives enough machinery to an interested reader to try his strength in this modern flourishing area.

-- Zentralblatt Math

#### Table of Contents

# Table of Contents

## Wave Packet Analysis

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface vii8 free
- Chapter 1. Introduction 110 free
- Chapter 2. Wavelets and square functions 514 free
- Chapter 3. Interpolation of multilinear operators 1524
- Chapter 4. Paraproducts 2332
- Chapter 5. Wave packets 3140
- Chapter 6. Multilinear forms with modulation symmetries 4150
- Chapter 7. Carleson's Theorem 5362
- Chapter 8. The Walsh model 6372
- Chapter 9. Further applications of wave packet analysis 7584
- Bibliography 8594
- Back Cover Back Cover197