The Characterization Of A Kind Of Multidimensional Real Variable Q-shaped Space

As a new space between W1,n(Rn)and BMO(Rn),since the 1990s,the Q-type space has been widely studied.So,this paper continues to study Q-type space.In this paper,we study a class of new space QK,?(Rn)obtained from Q??(Rn)space.Given n? 3,?>0 and K:[0,?)?[0,?)be a nondecreasing function.We say a function f ?Lloc2(Rn)is said to belong to QK,?(Rn)if where the supremum of the formula is taken over all cubes I with edge length l(I)and edges parallel to the coordinate axes in Rn.First,we investigate some basic properties of QK,?(Rn)spaces;next,we characterize QK,?(Rn)via a Carleson type measure associated with K;last,by the dyadic cubes,we prove a mean oscillation property of QK,?(Rn).This property enables us to establish the regular wavelet characterization of QK,?(Rn).