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Kyungpook Mathematical Journal 2020; 60(3): 519-534

Published online September 30, 2020

Copyright © Kyungpook Mathematical Journal.

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

Fariba Alighadr Ardebili, Hamid Vaezi*, Mostafa Hassanlou

Department of Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran
e-mail : faribaalighadr@gmail.com
Department of Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran and Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
e-mail : hvaezi@tabrizu.ac.ir
Technical Faculty of Khoy, Urmia University, Urmia, Iran
e-mail : M.hassanlou@urmia.ac.ir

Received: September 29, 2019; Accepted: March 20, 2020

Abstract

Let be the space of all holomorphic functions on the open unit disc in the complex plane ℂ. In this paper, we investigate the boundedness and compactness of the generalized integration operator Ig,ϕ(n)(f)(z)=0zf(n)(ϕ(ξ))g(ξ)dξ,         zD,

between Bloch-type and weighted Dirichlet-type spaces, where ϕ is a holomorphic self-map of , n ∈ ℕ and .

Keywords: integration operator, Bloch-type space, Dirichlet-type space