Some Relations And Extension Of Functional Spaces Q_p And Q_T

We introduce a new space Q_T space of analytic functions on the unit disk in terms of nondecreasing function T :[0,∞)→[0,∞), Where the g (z , a )= log(|(1-az)/(z-a)|)(z,a∈Δ) is the Green function whose the singular point is at a in the unit diskΔ.In the theses [A.L1] and [A.X.Z2], the space is introduced and studied,where the H (Δ) denotes the collection of the analytic functions in the unit disk.Now, the relation between the space Q_T and the space Q_p will be considered by studying the characteristics of T , including the growth order, integration and so on. Considering the relation between Q_T and Q_p spaces by studying the growth order of T has been discussed in the reference literature [W.W] written by H.Wulan and P. Wu.To this new function space Q_T composed of analytic functions on the unit disk where the T ( r )is nondecreasing function, we can consider the relation of the function space Q_T and the function space Q_p by studying the integration of T ( r ). At last, we can study the relation of function space Q_T and function space Q_p furthermore some results that we want will be gotten. Subsequently we will study the function space Q_T #and function space Q_p~#, which is corresponding to the function space Q_T and function space Q_p, and we can extend the conclusions that we have gotten.