Logarithmic (¦Á, ¦Â)-bloch Space On Operator Theory

The introduction of Blog,(α,β) and Qk (p.q) spaces enlarge the scope of the research of function space theory. The conclusions obtained are more extensive. This would give enormous impetus both to the development of this direction and to the research of some other related fields. In this paper, we mainly make a research on the properties of these two spaces from the following three aspects, and obtain the key results, which extends some known results.First, we discuss some basic properties of Blog(α,β) spaces on the unit disc, including integral properties of logarithmic (α,β)-Bloch spaces,corresponding integral properties of little logarithmic (α,β)-Bloch spaces and using Carless measure to charactering logarithmic(α,β)-Bloch spaces.Second, we characterize the boundedness and compactness of composition operators Cφon Blog(α,β) spaces.At last, we investigate the boundedness of weighted composition operators acting from different Bloch type spaces such as Bαspaces,Blogαspaces to QK(p,q) spaces, and give the necessary and sufficient condition.