Logarithmic Hardy-bloch Type Spaces And Related To Operator Theory

In this paper, based on Hardy space in the unit disk, we define two new spaces: the Logarithmic Hardy-Bloch space (DHαLp) and the little Logarithmic Hardy-Bloch space(DH_αL^pO).In Chapter 1, we mainly introduce the development of Hardy space in the unit disk and list some results to the thesis. We also introduce the definition of some analytic function spaces and the weighted composition operators.In Chapter 2, we concern study, whichα=1, the containment relation between Hardy spaces(Hp), Dirichlet type spaces(D_p-1^p) and VMOA space. When a> 1, A sufficient and necessary condition is given for any in f∈DH_αL^p,O(DH_αL^p,O). For given anyα≥1, we also obtain some estimates on the growth of f(z)=Σ_n=0^∞anzn∈DH_αL^p(DH_αL^p,O and its Taylor coefficient.In Chapter 3, we are devoted to investigate, whichα=1, some sufficient condi-tions and necessary conditions in weighted composition operator which is bounded or compact f∈DHLp from to Bloch space or little Bloch space. A sufficient and necessary condition is given for the composition operator to be bounded or compact on the Bloch space (or the little Bloch space).