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Let g be an analytic function on the open unit disk D in the complex plane C. We will study the following operator I g (h)(z):= ∫ z 0 h'(ζ)g(ζ)dζ, J g (h)(z) = ∫ z 0 h(ζ)g'(C)dζ on the Bloch space. In this paper, we will study the boundedness and compactness of I g on the α-Bloch space, and the boundedness and compactness of products of I g and J g defined on the α-Bloch space. And we will get the relationship of multiplication operator M g and the operators I g , J g defined on the α-Bloch space.

Multiplication operators, integration operatorsand companion operators on weighted Bloch space