Hausdorff dimension of functions on d-sets
 
 
Description:  The sharp upper bound for the Hausdorff dimension of the graphs of the functions in Holder and Besov spaces (in this case with integrability p\geq 1) on fractal d-sets is obtained: \min\{d+1-s,d/s\}, where s\in(0,1] denotes the smoothness parameter. In particular, when passing from d\geq 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.
Date:  2012-05-11
Start Time:   14:30
Speaker:  António Caetano (Univ. Aveiro)
Institution:  Univ. Aveiro
Place:  Sala 5.5
Research Groups: -Analysis
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A.Caetano-Abstract
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