CONTENTS

Chapter I. The Dirichlet Problem and Parabolic Measure 1

1. Introduction 1

2. Statement of Results 4

3. Basic Estimates 9

4. Proof of Theorem 2.13 in a Special Case 21

5. Proof of Theorem 2.13 34

6. References 45

Chapter II. Absolute Continuity and the LP Dirichlet Problem: Part 1 46

1. Introduction 46

2. Preliminary Reductions for Theorem 1.10 50

3. Lemmas on Parabolic Measure 61

4. Extrapolation 70

5. References 80

Chapter III. Absolute Continuity and the

Lp

Dirichlet Problem: Part 2 81

1. Introduction 81

2. Proof of Theorem 1.7 in a Special Case 83

3. Proof of Theorem 1.7 99

4. Elliptic Results 106

5. References 113