Caetano A.M. Homogeneity, non-smooth atoms and Besov spaces of generalised smoothness on quasi-metric spaces / Caetano A.M., Lopes S. - Warszawa, 2009. - 44 p. - (Dissertationes mathematicae; 2009-460) - ISSN 0012-3862  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Contents

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