• 호남수학학술지
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• 제37권4호
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• pp.387-395
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• 2015

We investigate conditions under which a holomorphic self-map of the unit disk induces a bounded composition operator and study some properties of the composition operator from the Bloch-type spaces into a generalization of the Bloch-type spaces.

• 대한수학회보
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• 제61권4호
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• pp.875-895
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• 2024

In this paper, we completely characterize the Schatten classes of composition operators on the Dirichlet type spaces with superharmonic weights. Our investigation is basced on building a bridge between the Schatten classes of composition operators on the weighted Dirichlet type spaces and Toeplitz operators on weighted Bergman spaces.

• 대한수학회논문집
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• 제29권3호
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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 < ${\alpha}$ < ${\infty}$).

• 대한수학회지
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• 제45권4호
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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.

• 대한수학회논문집
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• 제26권3호
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• pp.455-462
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• 2011

An analytic self-map ${\phi}$ of the open unit disk $\mathbb{D}$ in the complex plane and an analytic map ${\psi}$ on $\mathbb{D}$ induce the so-called weighted composition operator $C_{{\phi},{\psi}}$: $H(\mathbb{D})\;{\rightarrow}\;H(\mathbb{D})$, $f{\mapsto} \;{\psi}\;(f\;o\;{\phi})$, where H($\mathbb{D}$) denotes the set of all analytic functions on $\mathbb{D}$. We study when such an operator acting between different weighted Bergman spaces is bounded, compact and Schatten class.

• 대한수학회보
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• 제60권5호
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• pp.1141-1154
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• 2023

In this paper, we study the complex symmetric weighted composition-differentiation operator D_𝜓,𝜙 with respect to the conjugation JW_𝜉,𝜏 on the Hardy space H². As an application, we characterize the necessary and sufficient conditions for such an operator to be normal under some mild conditions. Finally, the spectrum of D_𝜓,𝜙 is also investigated.

• 대한수학회보
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• 제60권3호
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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].

• 대한수학회논문집
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• 제38권4호
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• pp.1075-1090
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• 2023

In this paper, we study new classes of operators k-quasi (m, n)-paranormal operator, k-quasi (m, n)^*-paranormal operator, k-quasi (m, n)-class 𝒬 operator and k-quasi (m, n)-class 𝒬^* operator which are the generalization of (m, n)-paranormal and (m, n)^*-paranormal operators. We give matrix characterizations for k-quasi (m, n)-paranormal and k-quasi (m, n)^*-paranormal operators. Also we study some properties of k-quasi (m, n)-class 𝒬 operator and k-quasi (m, n)-class 𝒬^* operators. Moreover, these classes of composition operators on L² spaces are characterized.

• 대한수학회지
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• 제48권5호
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• pp.969-984
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• 2011

This paper discusses the hypercyclicity of weighted composition operators acting on the space of holomorphic functions on the open unit ball $B_N$ of $\mathbb{C}^N$. Several analytic properties of linear fractional self-maps of $B_N$ are given. According to these properties, a few necessary conditions for a weighted composition operator to be hypercyclic in the space of holomorphic functions are proved. Besides, the hypercyclicity of adjoint of weighted composition operators are studied in this paper.

• 대한수학회논문집
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• 제18권4호
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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.