On Logarithmic (α,β)-Bloch Spaces And Q_K(p,q) Spaces

There are two parts in this paper. In part one, we define and study the log B(α/β) spaces. The following are our main results in this part:1. Characterize the Taylor coefficients of analytic functions in the spaces log B(α,β) and log B(α,β).2. Study the relationship between log B (α,β) spaces and Cesaro means and show thatsup{||σ_n(f)||log B(α,β) : n ∈ N ∪ {0}} = ||f||log B(α,β)In part two, by applying the theory and methods in Q_K spaces, we consider a general Q_k type spaces Q_k(p,q) and their subspaces Q_k,o(p,q). Our main results are stated as follows:1. Tow sufficient conditions for f∈Q_k,O(p,q) are given.2. A sufficient condition for Q_k(p,q) = log B(β+(q+2)/p,β) is proved.