|
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.
|
