| Preface 0. Background 0.1. Fourier Transform 0.2. Basic Real Variable Theory 0.3. Fractional Integration and Sobolev Embedding Theorems 0.4. Wave Front Sets and the Cotangent Bundle 0.5. Oscillatory Integrals Notes 1. Stationary Phase 1.1. Stationary Phase Estimates 1.2. Fourier Transform of Surface-carried Measures Notes 2. Non-homogeneous Oscillatory Integral Operators 2.1. Non-degenerate Oscillatory Integral Operators 2.2. Oscillatory Integral Operators Related to the Restriction Theorem 2.3. Riesz Means in R" 2.4. Kakeya Maximal Functions and Maximal Riesz Means in R2 Notes 3. Pseudo-differential Operators 3.1. Some Basics 3.2. Equivalence of Phase Functions 3.3. Self-adjoint Elliptic Pseudo-differential Operators on Compact Manifolds Notes 4. The Half-wave Operator and Functions of Pseudo-differential Operators 4.1. The Half-wave Operator 4.2. The Sharp Weyl Formula 4.3. Smooth Functions of Pseudo-differential Operators Notes 5. LP Estimates of Eigenfunctions 5.1. The Discrete L2 Restriction Theorem 5.2. Estimates for Riesz Means 5.3. More General Multiplier Theorems Notes 6. Fourier Integral Operators 6.1. Lagrangian Distributions 6.2. Regularity Properties 6.3. Spherical Maximal Theorems: Take 1 Notes 7. Local Smoothing of Fourier Integral Operators 7.1. Local Smoothing in Two Dimensions and Variable Coefficient Kakeya Maximal Theorems 7.2. Local Smoothing in Higher Dimensions 7.3. Spherical Maximal Theorems Revisited Notes Appendix: Lagrangian Subspaces of T*IRn Bibliography Index Index of Notation |
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