Contents Preface to the English edition vii General introduction 1 Chapter 0. Notation and review of distribution theory 5 §1. Spaces of differentiate functions and differential operators 5 §2. Distributions on an open set of E n 6 §3. Convolution 8 §4. Kernels 9 §5. Fourier analysis on Mn 10 Chapter I. Pseudo-differential operators 15 §1. Introduction 15 §2. Symbols 20 §3. Pseudo-differential operators in S and Sf 24 §4. Composition of operators 28 §5. Action of pseudo-differential operators and Sobolev spaces 29 §6. Operators in an open subset of Rn 34 §7. Operators on a manifold 37 §8. Appendix 41 Commentary on Chapter I 49 Exercises for Chapter I 50 Chapter II. Nonlinear dyadic analysis, microlocal analysis, energy estimates 77
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