Classic and Exotic Besov Spaces Induced by Good Grids

In a previous work we introduced Besov spaces ℬ^s_p,q defined on a measure space with a good grid, with p∈ [1,∞ ) , q∈ [1,∞ ] 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.