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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 Moura. Function spaces of generalised smoothness. 2001. <http://eudml.org/doc/286057>.
@book{SusanaDominguesdeMoura2001, abstract = {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.}, author = {Susana Domingues de Moura}, keywords = {Besov space; Triebel-Lizorkin space; generalised smoothness; entropy numbers; fractal; Carl's inequality}, language = {eng}, title = {Function spaces of generalised smoothness}, url = {http://eudml.org/doc/286057}, year = {2001}, }
TY - BOOK AU - Susana Domingues de Moura TI - Function spaces of generalised smoothness PY - 2001 AB - 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. LA - eng KW - Besov space; Triebel-Lizorkin space; generalised smoothness; entropy numbers; fractal; Carl's inequality UR - http://eudml.org/doc/286057 ER -
