Please, anyone of you know a simple example of a function which belongs to the Besov Space with $p=q=\infty$ and $s=0$ (over $\mathbb{R}$ or $I\subset\mathbb{R}$ where $I$ is a closed interval). I think that the function given by $$ \frac{1}{\log{\frac{1}{|x|^{\alpha}}}} $$ (perhaps just looking for a good $\alpha$) belongs to such space but I really don't know how to do the check.

In the other hand, and in the same way as above, some of you knows a kind of Weierstrass function, Takagi function, Minkowski question mark function,... such that it belongs to the Besov Space with $p=q=\infty$ and $s=0$?

Thanks in advance!

notbelong in certain other subspace of $B^{0,\infty}_\infty$, otherwise there are a lot of trivial examples. – Willie Wong Aug 31 '12 at 11:58