• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.653-659
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• 2003

Let $1{\;}\leq{\;}p{\;}\infty{\;}and{\;}{\alpha}{\;}>{\;}-1$. If f is a holomorphic self-map of the open unit disc U of C with f(0) = 0, then the quantity $\int_U\;\{\frac{$\mid$f'(z)$\mid$}{1\;-\;$\mid$f(z)$\mid$^2}\}^p\;(1\;-\;$\mid$z$\mid$)^{\alpha+p}dxdy$ is equivalent to the operator norm of the composition operator $C_f{\;}:{\;}B{\;}\rightarrow{\;}A^{p,{\alpha}$ defined by $C_fh{\;}={\;}h{\;}\circ{\;}f{\;}-{\;}h(0)$, where B and $A^{p,{\alpha}$ are the Bloch space and the weighted Bergman space on U respectively.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.429-441
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• 2020

Let M(X, Y) denote the space of multipliers from X to Y, where X and Y are analytic function spaces. As we known, for Dirichlet-type spaces 𝓓_α^p, M(𝓓_p-1^p, 𝓓_q-1^q) = {0}, if p ≠ q, 0 < p, q < ∞. If 0 < p, q < ∞, p ≠ q, 0 < s < 1 such that p + s, q + s > 1, then M(𝓓_p-2+s^p, 𝓓_q-2+s^q) = {0}. However, X ∩ 𝓓_p-1^p ⊆ X ∩ 𝓓_q-1^q and X ∩ 𝓓_p-2+s^p ⊆ X ∩ 𝓓_q-2+s^p whenever X is a subspace of the Bloch space 𝓑 and 0 < p ≤ q < ∞. This says that the set of multipliers M(X ∩ 𝓓 _p-2+s^p, X∩𝓓_q-2+s^q) is nontrivial. In this paper, we study the multipliers M(X ∩ 𝓓_p-2+s^p, X ∩ 𝓓_q-2+s^q) for distinct classical subspaces X of the Bloch space 𝓑, where X = 𝓑, BMOA or 𝓗^∞.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.57-66
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• 2009

In this paper, we characterize the boundedness and compactness of the extended $Ces{\grave{a}}ro$ operators from general function spaces F(p, q, s) to Bloch-type spaces ${\mathcal{B}}_{\mu}$ where $\mu$ is normal function on [0,1).

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.17-22
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• 1997

Let B be the open unit ball in the complex space $\mathbb{C}^n$. A holomorphic function $f:B{\rightarrow}C$ which satisfies sup{(1- ${\parallel}\;{\nabla}_zf\;{\parallel}\;{\mid}z{\in}B$} < $+{\infty}$ is called Bloch type function. In this paper, we will find some integral representation of Bloch type functions.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.649-657
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• 2023

In this paper, we give new necessary and sufficient conditions for the compactness of composition operator on the Besov space and the Bloch space of the unit ball, which, to a certain extent, generalizes the results given by M. Tjani in [10].

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.519-534
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• 2020

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).

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.185-200
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• 2013

We study the bounded and the compact weighted composition operators from the Hardy space $H^{\infty}$ into BMOA and into VMOA, from BMOA into $H^{\infty}$, as well as from BMOA into the Bloch space. We also provide new boundedness and compactness criteria for the weighted composition operators on BMOA and on VMOA.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.307-317
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• 2004

In the setting of the half-plane of the complex plane, we show that for $r\geq0$, the dual space of the weighted bergman spaces B$^{1}{\gamma}$ is the Bloch space of the half-plane and we study some bounded linear operators induced by radial derivatives.

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.277-287
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• 2002

Let B be the open unit ball with center 0 in the complex space $C^n$. For each q>0, B$_{q}$ consists of holomorphic functions f : B longrightarrow C which satisfy sup z $\in$ B $(1-\parallel z \parallel^2)^q\parallel\nabla f(z)\parallel < \infty$ In this paper, we will show that functions in weighted Bloch spaces $B_{q}$ (0 < q < 1) satifies the following Lipschitz type result for Bergman metric $\beta$: ｜f(z)-f($\omega$)｜< $C\beta$(z, $\omega$) for some constant C.