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 On the Hausdorff Dimension of Continuous Functions Belonging to Hölder and Besov Spaces on Fractal d-Sets
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/5559

title: On the Hausdorff Dimension of Continuous Functions Belonging to Hölder and Besov Spaces on Fractal d-Sets
authors: Carvalho, A.
Caetano, A.
keywords: Besov spaces
Box counting dimension
Continuous functions
d-Sets
Fractals
Hausdorff dimension
Hölder spaces
Wavelets
Weierstrass function
issue date: 2011
publisher: Springer
abstract: The Hausdorff dimension of the graphs of the functions in Hölder and Besov spaces (in this case with integrability p≥1) on fractal d-sets is studied. Denoting by s in (0,1] the smoothness parameter, the sharp upper bound min{d+1-s, d/s} is obtained. In particular, when passing from d≥s to d<s there is a change of behaviour from d+1-s to d/s which implies that even highly nonsmooth functions defined on cubes in ℝn have not so rough graphs when restricted to, say, rarefied fractals. © 2011 Springer Science+Business Media, LLC.
URI: http://hdl.handle.net/10773/5559
ISSN: 1069-5869
source: Journal of Fourier Analysis and Applications
appears in collectionsMAT - Artigos

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