  In a previous work we introduced Besov spaces $\mathcal{B}^s_{p,q}$ defined
on a measure spaces with a good grid, with $p\in [1,\infty)$, $q\in [1,\infty]$
and $0< s< 1/p$. Here we show that classical Besov spaces on compact
homogeneous spaces are examples of such Besov spaces. On the other hand we show
that even Besov spaces defined by a good grid made of partitions by intervals
may differ from a classical Besov space, giving birth to exotic Besov spaces.
