Q_K Type Spaces Of Analytic Functions

By applying the theory and methods in Q_k spaces, we study a general Q_k type spaces Q_k(p, q) and its subspaceQ_k,0(p, q) , which not only extend Q_k space to B^α spaces but also provide a new method to study B^α and its subspaces.A brief developing history of function spaces is given in chapter one and the spaces Q_k(p,q) of analytic in the unit disk are introduced. In chapter two we study the properties of Q_k(p, q) spaces . The main results in the thesis are stated as follows:1. Q_K(p,q) (?)B^[(q+2)/p], Q_K,0(p,q) (?) B₀^[(q+2)/p].2. Criteria for Q_k{p, q) = B^[(q+2)/p] and Q_k,0(p,q) = B_<sup>[(q+2)/p] are given.3. The nondecreasing K can be chosen as bounded.4. A sufficient condition for Q_k1(p,q) (?) Q_k2(p,q) is given.5. The polynomials belong to Q_k,0(p,q) spaces.