Lectures on Bochner-Riesz Means

by Katherine Michelle Davis , Yang-Chun Chang

• ISBN13: 9780521312776
• ISBN10: 0521312779
• Format: Paperback
• Copyright: 1987-11-27
• Publisher: Cambridge University Press

Summary

This book is concerned with the modern theory of Fourier series. Treating developments since Zygmund's classic study, the authors begin with a thorough discussion of the classical one-dimensional theory from a modern perspective. The text then takes up the developments of the 1970s, beginning with Fefferman's famous disc counterexample. The culminating chapter presents Cordoba's geometric theory of Kayeka maximal functions and multipliers. Research workers in the fields of Fourier analysis and harmonic analysis will find this a valuable account of these developments. Second year graduate students, who are familiar with Lebesgue theory and are acquainted with distributions, will be able to use this as a textbook which will bring them up to the exciting open questions in the field.

Table of Contents

Introduction

Preliminaries

1. Multiplier theory

2. The Hilbert transform

3. Good lambda and weighted norm inequalities

4. Multipliers with singularities

5. Singularities along curves

6. Restriction theorems

7. The multiplier theorem for the disc

8. The Cordoba multiplier theorem

References

Index.