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Generalized Integration Operator between the Bloch-type Space and Weighted Dirichlet-type Spaces

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Let H(D) be the space of all holomorphic functions on the open unit disc D in the complex plane C. In this paper, we investigate the boundedness and compactness of the generalized integration operatorI(n)g,ϕ(f)(z) = Z0f(n)(ϕ(ξ))g(ξ) dξ, z ∈ D, between Bloch-type and weighted Dirichlet-type spaces, where ϕ is a holomorphic self-map of D, n ∈ N and g ∈ H(D).

Abstract

Let H(D) be the space of all holomorphic functions on the open unit disc D in the complex plane C. In this paper, we investigate the boundedness and compactness of the generalized integration operatorI(n)g,ϕ(f)(z) = Z0f(n)(ϕ(ξ))g(ξ) dξ, z ∈ D, between Bloch-type and weighted Dirichlet-type spaces, where ϕ is a holomorphic self-map of D, n ∈ N and g ∈ H(D).

참고문헌 (24)

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