The structure of functions

Front Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 12
1 Introduction, heuristics, and preliminaries ......Page 14
2 Spaces on R^n: the regular case ......Page 23
3 Spaces on R^n: the general case ......Page 40
4 An application: the Fubini property ......Page 47
5 Spaces on domains: localization and Hardy inequalities ......Page 54
6 Spaces on domains: decompositions ......Page 84
7 Spaces on manifolds   ......Page 94
9 fraces on sets, related function spaces and their decompositions ......Page 133
10 Introduction: Outline of methods and results ......Page 174
11 Classical inequalities ......Page 180
12 Envelopes             ......Page 194
13 The critical case ......Page 215
14 The super-critical case ......Page 231
15 The sub-critical case ......Page 242
16 Hardy inequalities ......Page 248
17 Complements ......Page 256
18 Introduction ......Page 264
19 Spectral theory for the fractal Laplacian ......Page 266
20 The fractal Dirichiet problem ......Page 307
21 Spectral theory on miinifolds ......Page 323
22 Isotropic fractals and related function spaces ......Page 342
23 Isotropic fractal drums ......Page 361
24 Introduction ......Page 368
25 Truncations ......Page 370
26 The Q-operator ......Page 398
References ......Page 416
Symbols ......Page 432
Index ......Page 436