The structure of functions

InhaltsverzeichnisI Decompositions of Functions.1 Introduction, heuristics, and preliminaries.2 Spaces on ? n: the regular case.3 Spaces on ? n: the general case.4 An application: the Fubini property.5 Spaces on domains: localization and Hardy inequalities.6 Spaces on domains. decompositions.7 Spaces on manifolds.8 Taylor expansions of distributions.9 Traces on sets, related function spaces and their decompositions.II Sharp Inequalities.10 Introduction: Outline of methods and results.11 Classical inequalities.12 Envelopes.13 The critical case.14 The super-critical case.15 The sub-critical case.16 Hardy inequalities.17 Complements.III Fractal Elliptic Operators.18 Introduction.19 Spectral theory for the fractal Laplacian.20 The fractal Dirichlet problem.21 Spectral theory on manifolds.22 Isotropic fractals and related function spaces.23 Isotropic fractal drums.IV Truncations and Semi-linear Equations.24 Introduction.25 Truncations.26 The Q-operator.27 Semi-linear equations; the Q-method.References.Symbois.