- October 26, 2012, Friday - 14h30 (Room P
3.10):
António Caetano
(Universidade de Aveiro)
"
Hausdorff Dimension of Functions on d-sets "
Abstract. The
sharp upper bound for the Hausdorff dimension of the graphs of the
functions in Hölder and Besov spaces (in this case with
integrability \(p\ge 1\)) 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 \(d\ge s\) to \(s>d\)
there is a change of behavior from \(d+1-s\) to \(d/s\) which implies
that even highly nonsmooth functions defined on cubes in
\(\mathbb{R}^n\) have not so rough graphs when restricted to, say, rarefied fractals.
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