Function spaces of generalised smoothness

Volume 398 / 2001

Susana Domingues de Moura Dissertationes Mathematicae 398 (2001), 1-88 MSC: 28A78, 28A80, 35P15, 46E30, 46E35, 47B06 DOI: 10.4064/dm398-0-1


We study spaces of generalised smoothness of Besov and Triebel–Lizorkin type. In particular, we get characterisations by local means, atomic and subatomic representations. These results are applied to estimate the entropy numbers of compact embeddings between function spaces on fractals. Due to Carl's inequality this is useful in the study of the behaviour of eigenvalues in problems which correspond to the vibrations of a drum, the whole mass of which is concentrated on a fractal subset of the drum.


  • Susana Domingues de MouraDepartamento de Matemática
    Universidade de Coimbra
    Apartado 3008
    3001-454 Coimbra, Portugal

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