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 |
Author: | 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. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/5559 |
ISSN: | 1069-5869 |
Appears in Collections: | DMat - Artigos |
Files in This Item:
File | Description | Size | Format | |
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11044.pdf | Documento principal | 437.46 kB | Adobe PDF | View/Open |
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