On the Hausdorff dimension of continuous functions belonging to Hölder and Besov spaces on fractal d-sets

Details On the Hausdorff dimension of continuous functions belonging to Hölder and Besov spaces on fractal d-sets On the Hausdorff dimension of continuous functions belonging to Hölder and Besov spaces on fractal d-sets

2010-12-30

arxiv.org/abs/1101.0147v1

Mathematics

Functional Analysis

25 pages, preprint

Scientific paper

The Hausdorff dimension of the graphs of the functions in H\"older and Besov spaces (in this case with integrability p \geq 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 \geq s to d