Lectures on Bochner-Riesz Means (London Mathematical Society Lecture Note Series, Series Number 114)

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. Katherine Michelle Davis, Yang-chun Chang. Includes Index. Bibliography: P. 147-148. Cover Series Page Title Copyright Dedication CONTENTS INTRODUCTION CHAPTER 0 0.1 INTRODUCTION 0.2 THE ROLE OF FUNCTIONAL ANALYSIS 0.3 BACKGROUND 0.4 NOTES FOR CHAPTER 0 CHAPTER 1 MULTIPLIER THEORY SECTION 1.1 MULTIPLIERS ON LP SECTION 1.2 MULTIPLIERS ON LP SECTION 1.3 MULTIPLIERS AND SUMMABILITY OF SERIES SECTION 1.4 REMARKS FOR CHAPTER 1 CHAPTER 2 THE HILBERT TRANSFORM SECTION 2.1 INTRODUCTION SECTION 2.2 THE HILBERT TRANSFORM SECTION 2.3 COTLAR'S THEOREM SECTION 2.4 THE HARDY-LITTLEWOOD MAXIMAL FUNCTION SECTION 2.5 THE MAXIMAL HILBERT TRANSFORM SECTION 2.6 REMARKS FOR CHAPTER 2 CHAPTER 3 GOOD . AND WEIGHTED NORM INEQUALITIES SECTION 3.1 GOOD . INEQUALITIES SECTION 3.2 THE Ap CONDITION SECTION 3.3 WEIGHTED NORM INEQUALITIES SECTION 3.4 REMARKS FOR CHAPTER 3 CHAPTER 4 MULTIPLIERS WITH SINGULARITIES SECTION 4.1 THE HORMANDER-MIHILIN THEOREM SECTION 4.2 THE LITTLEWOOD PALEY AND MARCINKIEWICZ THEOREMS SECTION 4.3 REMARKS AND EXTENSIONS CHAPTER 5 SINGULARITIES ALONG CURVES SECTION 5.1 ASYMPTOTICS OF BESSEL FUNCTIONS SECTION 5.2 A THEOREM OF DELEEUW AND STEIN SECTION 5.4 REMARKS AND EXTENSIONS CHAPTER 6 RESTRICTION THEOREMS SECTION 6.1 RESTRICTION SECTION 6.2 BOCHNER-RIESZ MEANS SECTION 6.3 EXTENSIONS AND REMARKS CHAPTER 7 THE MULTIPLIER PROBLEM FOR THE DISC SECTION 7.1 MEYER'S LEMMA SECTION 7.2 THE KAKEYA SET SECTION 7.3 EXTENSIONS AND REMARKS CHAPTER 8 THE CORDOBA MULTIPLIER THEOREM SECTION 8.1 ALMOST ORTHOGONALITY SECTION 8.2 THE CORDOBA MAXIMAL FUNCTION SECTION 8.3 THE CORDOBA MULTIPLIER THEOREM SECTION 8.4 RESTRICTION REVISITED SECTION 8.5 REMARKS AND EXTENSIONS REFERENCES INDEX