The α-modulation spaces M p,q , introduced by Gröbner in [10] are a class of function spaces that contain Besov spaces B p,q (α = 1) and modulation spaces M s p,q (α = 0) as special cases. There are two kinds of basic coverings on Euclidean R which is very useful in the theory of function spaces and their applications, one is the uniform covering R = ⋃ k∈Zn Qk, where Qk denote the unit cube wit...