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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