Multipliers and Cyclic Vectors in Bloch Type Spaces

Abstract

In this paper we study the coefficient multipliers, pointwise multipliers and cyclic vectors in the Bloch type spaces Bα and little Bloch type spaces \( B^{\alpha }_{0} \) for 0 < α < ∞. We give several full characterizations of the coefficient multipliers (Bα,Bβ) and \( {\left( {B^{\alpha }_{0} ,B^{\beta }_{0} } \right)} \) for 0 < α, β < ∞ and pointwise multipliers M(Bα,Bβ) and \( M{\left( {B^{\alpha }_{0} ,B^{\beta }_{0} } \right)} \) for 1 ≠ α, β ∈ (0,∞). We also obtain some properties of cyclic vectors for Bloch type spaces.