1. Introduction ................................................. 5
2. Preliminaries ................................................ 7
2.1. General notation ........................................ 7
2.2. Admissible sequences and functions ...................... 8
3. Besov spaces of generalised smoothness on Rn ................ 11
3.1. The Fourier-analytic approach .......................... 11
3.2. Characterisation by smooth atomic decompositions ....... 12
3.3. Characterisation by differences and homogeneity ........ 14
3.4. Characterisation by non-smooth atomic decompositions ... 22
4. Besov spaces of generalised smoothness on h-sets ............ 25
4.1. h-sets ................................................. 25
4.2. Characterisation by atomic decompositions .............. 28
5. Besov spaces on quasi-metric spaces ......................... 36
5.1. Quasi-metric spaces and Euclidean charts ............... 36
5.2. Function spaces on h-spaces ............................ 38
5.3. Example: entropy numbers ............................... 42
References ..................................................... 43
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