• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.349-357
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• 1996

Using a special property of Bloch functions with Hardmard gaps and using the geometric properties of the self maps of the unit disc, we give a way of constructing explicit examples of Bloch functions f whose derivative is in $H^p$ (0 < p < 1) but $f \notin BMOA$.

• 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.49 no.1
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• pp.11-24
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• 2012

We characterize the class of inner uniform domains in terms of the quasihyperbolic metric and the quasihyperbolic geodesic. We also characterize uniform domains and inner uniform domains in terms of weak Bloch functions.

• East Asian mathematical journal
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• v.9 no.2
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• pp.313-319
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• 1993

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.1071-1074
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• 2012

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.475-482
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• 2007

In this paper, we study composition operators $C_{\varph}f=f^{\circ}{\varph}$, induced by a fixed analytic self-map of the of the upper half-plane, acting between Hardy and Bloch-type spaces of the upper half-plane.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.409-413
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• 2014

In this paper, we study some quantity equivalent to the norm of Bloch to $A^p_{\alpha}$ composition operator where Ap $A^p_{\alpha}$ is the weighted Bergman space on the unit ball of $\mathbb{C}^n$ (0 < p < ${\infty}$ and -1 < ${\alpha}$ < ${\infty}$).

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.977-991
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• 2008

We characterize the boundedness and compactness of the weighted composition operator $uC_{\psi}$ from the general function space F(p, q, s) into the logarithmic Bloch space ${\beta}_L$ on the unit disk. Some necessary and sufficient conditions are given for which $uC_{\psi}$ is a bounded or a compact operator from F(p,q,s), $F_0$(p,q,s) into ${\beta}_L$, ${\beta}_L^0$ respectively.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.751-759
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• 2015

In this paper, we give new characterizations of the boundedness and compactness of composition operators $C_{\varphi}$ between Bloch type spaces in the unit ball $\mathbb{B}^n$, in terms of the power of the components of ${\varphi}$, where ${\varphi}$ is a holomorphic self-map of $\mathbb{B}^n$.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.703-708
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• 2005

Let ${\varphi}(z)\;=\;({\varphi}_1(Z),{\cdots},{\varphi}_n(Z))$ be a holomorphic self­map of $\mathbb{D}^n$, where $\mathbb{D}^n$ is the unit polydisk of $\mathbb{C}^n$. The sufficient and necessary conditions for a composition operator to be bounded and compact from the Hardy space $H^2(\mathbb{D}^n)$ into $\alpha$-Bloch space $\beta^{\alpha}(\mathbb{D}^n)$ on the polydisk are given.