• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.287-292
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• 2006

On the unit disk of the complex plane, a characterization of Bloch function is expressed extending known result.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.85-103
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• 2015

We prove some sharp extremal distance results for functions in various spaces of analytic functions on bounded strictly pseudoconvex domains with smooth boundary. Also, we obtain atomic decompositions in multifunctional Bloch and weighted Bergman spaces of analytic functions on strictly pseudoconvex domains with smooth boundary, which extend known results in the classical case of a single function.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.373-382
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• 2007

In this paper, we characterize the boundedness and compactness of weighted composition operators ${\psi}C{\varphi}f=\psi(f^{\circ}\varphi)$ acting between Bergman and Bloch spaces of holomorphic functions on the open unit disk D.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1337-1346
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• 2017

We define Bloch-type spaces of ${\mathcal{C}}^1({\mathbb{H}})$ on the upper half plane H and characterize them in terms of weighted Lipschitz functions. We also discuss the boundedness of a composition operator ${\mathcal{C}}_{\phi}$ acting between two Bloch spaces. These obtained results generalize the corresponding known ones to the setting of upper half plane.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.543-552
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• 2012

In this paper, we will show that if ${\mu}$ is a Borel measure on the unit disk D such that ${\int}_{D}\frac{d{\mu}(z)}{(1-\left|z\right|^2)^{p\alpha}}$ < ${\infty}$ where 0 < ${\alpha},{\rho}$ < ${\infty}$, then a bounded sequence of functions {$f_n$} in the $\alpha$-Bloch space $\mathcal{B}{\alpha}$ has a convergent subsequence in the space $D_p({\mu})$ of analytic functions f on D satisfying $f^{\prime}\;{\in}\;L^p(D,{\mu})$. Also, we will find some conditions such that ${\int}_D\frac{d\mu(z)}{(1-\left|z\right|^2)^p$.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.567-578
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• 2017

Many scholars studied the boundedness of $Ces{\grave{a}}ro$ operators between $Q_K$ spaces and Bloch spaces of holomorphic functions in the unit disc in the complex plane, however, they did not describe the compactness. Let 0 < ${\alpha}$ < $+{\infty}$, K(r) be right continuous nondecreasing functions on (0, $+{\infty}$) and satisfy $${\displaystyle\smashmargin{2}{\int\nolimits_0}^{\frac{1}{e}}}K({\log}{\frac{1}{r}})rdr<+{\infty}$$. Suppose g is a holomorphic function in the unit disk. In this paper, some sufficient and necessary conditions for the extended $Ces{\grave{a}}ro$ operators $T_g$ between ${\alpha}$-Bloch spaces and $Q_K$ spaces in the unit disc to be bounded and compact are obtained.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.581-594
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• 2019

In this study a new generalization for operators of two parameters type of fractional in the unit disk is proposed. The fractional operators in this generalization are in the Srivastava-Owa sense. Concerning with the related applications, the generalized Gauss hypergeometric function is introduced. Further, some boundedness properties on Bloch space are also discussed.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1219-1232
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• 2009

Let H(B) denote the space of all holomorphic functions on the unit ball B of $\mathbb{C}^n$. Let $\varphi$ = (${\varphi}_1,{\ldots}{\varphi}_n$) be a holomorphic self-map of B and $g{\in}2$(B) with g(0) = 0. In this paper we study the boundedness and compactness of the generalized composition operator $C_{\varphi}^gf(z)=\int_{0}^{1}{\mathfrak{R}}f(\varphi(tz))g(tz){\frac{dt}{t}}$ from generalized weighted Bergman spaces into Bloch type spaces.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.159-165
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• 2010

A characterization of the holomorphic function spaces of mean Bloch type on the unit disc is deduced in terms of the induced distance.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.495-506
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• 2019

Motivated by Bloch's principle, we prove a value distribution result for meromorphic functions which is related to Hayman's alternative in certain sense.