1 Historical Background 1
2 The Lebesgue Measure,Convolution 9
3 Smoothing by Convolution 15
4 Truncation;Radon Measures;Distributions 17
5 Sobolev Spaces;Multiplication by Smooth Functions 21
6 Density of Tensor Products;Consequences 27
7 Extending the Notion of Support 33
8 Sobolev's Embedding Theorem,1≤P<N 37
9 Sobolev'Embedding Theorem,N≤P≤∞ 43
10 Poincaré's Inequality 49
11 The Equivalence Lemma;Compact Embeddings 53
12 Regularity of the Boundary;Consequences 59
13 Traces on the Boundary 65
14 Green's Formula 69
15 The Fourier Transform 73
16 Traces of H8(RN) 81
17 Proving that a Point is too Small 85
18 Compact Embeddings 89
19 Lax-Milgram Lemma 93
20 The Space H(div;Ω) 99
21 Background on Interpolation;the Complex Method 103
22 Real Interpolation;K-Method 109
23 Interpolation of L2 Spaces with Weights 115
24 Real Interpolation;J-Method 119
25 Interpolation Inequalities,the Spaces(E0,E1)θ,1 123
26 The Lions-Peetre Reiteration Theorem 127
27 Maximal Functions 131
28 Bilinear and Nonlinear Interpolation 137
29 Obtaining Lp by Interpolation,with the Exact Norm 141
30 My Approach to Sobolev's Embedding Theorem 145
31 My Generalization of Sobolev's Embedding Theorem 149
32 Sobolev's Embedding Theorem for Besov Spaces 155
33 The Lions-Magenes Space H1/2 00(Ω) 159
34 Defining Sobolev Spaces and Besov Spaces for Ω 163
35 Characterization of W8,p(RN) 165
36 Characterization of W8,p(Ω) 169
37 Variants with BV Spaces 173
38 Replacing BV by Interpolation Spaces 177
39 Shocks for Quasi-Linear Hyperbolic Systems 183
40 Interpolation Spaces as Trace Spaces 191
41 Duality and Compactness for Interpolation Spaces 195
42 Miscellaneous Questions 199
43 Biographical Information 205
44 Abbreviations and Mathematical Notation 209
References 213
Index 215