1 historical background
2 the lebesgue measure, convolution
3 smoothing by convolution
4 truncation; radon measures; distributions
5 sobolev spaces; multiplication by smooth functions
6 density of tensor products; consequences
7 extending the notion of support
8 sobolev''s embedding theorem, i ≤ p ＜ n
9 sobolev''s embedding theorem, n ≤ p≤∞
10 poincare''s inequality
11 the equivalence lemma; compact embeddings
12 regularity of the boundary; consequences
13 traces on the boundary
14 green''s formula
15 the fourier transform
16 traces of hsrn
17 proving that a point is too small
18 compact embeddings
19 lax-milgram lemma
.20 the space hdiv;
ω
21 background on interpolation; the complex method
22 real interpolation; k-method
23 interpolation of l2 spaces with weights
24 real interpolation; j-method
25 interpolation inequalities, the spaces e0, e1θ,1
26 the lions-peetre reiteration theorem
27 maximal functions
28 bilinear and nonlinear interpolation
29 obtaining lp by interpolation, with the exact norm
30 my approach to sobolev''s embedding theorem
31 my generalization of sobolev''s embedding theorem
32 sobolev''s embedding theorem for besov spaces
33 the lions-magenes space h12∞ω
34 defining sobolev spaces and besov spaces for ω
35 characterization of ws,prn
36 characterization of ws,pω
37 variants with bv spaces
38 replacing bv by interpolation spaces
39 shocks for quasi-linear hyperbolic systems
40 interpolation spaces as trace spaces
41 duality and compactness for interpolation spaces
42 miscellaneous questions
43 biographical information
44 abbreviations and mathematical notation
references
index
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