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http://dx.doi.org/10.5666/KMJ.2020.60.3.519

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

Ardebili, Fariba Alighadr (Department of Mathematics, Sarab Branch, Islamic Azad University)
Vaezi, Hamid (Department of Mathematics, Sarab Branch, Islamic Azad University)
Hassanlou, Mostafa (Technical Faculty of Khoy, Urmia University)
Publication Information
Kyungpook Mathematical Journal / v.60, no.3, 2020 , pp. 519-534 More about this Journal
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 operator $$I^{(n)}_{g,{\varphi}}(f)(z)=\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^z\;f^{(n)}({\varphi}({\xi}))g({\xi})\;d{\xi},\;z{\in}{\mathbb{D}},$$ between Bloch-type and weighted Dirichlet-type spaces, where 𝜑 is a holomorphic self-map of 𝔻, n ∈ ℕ and g ∈ H(𝔻).
Keywords
generalized integration operator; Bloch-type space; Dirichlet-type space;
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