Hadamard Product In Lipschitz Spaces And Some Results Of Q_k Spaces

In this paper, we mainly study the Hadamard product in A(q,α) and (?)~αspaces. Then, we discuss some predecessor's results without monotony of K(r)in Q_K spaces.The thesis consists of the following three parts:The first part focuses on recalling some backgrounds of function spacesand operators; At the same time, we give some definitions and relationshipsamong several classical function spaces; Furtherly, we introduce several quitenew function spaces, for example, F(p, q,s),Q_P, Q_K,(?)~αand so on;Finally, we list a few useful signs,functions and lemmas.In the second part, we get some characterizations of the Hadamard prod-uct in A (g,α) and (?)~αspaces on the basis of two articles of M. Mateljevicand M. Pavlovic using the relation among Young's inequality,M_p(r,f) andM_p(r,f').In the third part, we first introduce some elementary knowledges in Q_Kspaces, and then consider some relations between Q_K spaces and some classicfunction spaces when we remove the monotony of K(r).