• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1195-1205
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• 2011

Let $H(\mathbb{D})$ denote the class of all analytic functions on the open unit disk $\mathbb{D}$ of the complex plane $\mathbb{C}$. Let n be a nonnegative integer, ${\varphi}$ be an analytic self-map of $\mathbb{D}$ and $u{\in}H(\mathbb{D})$. The generalized weighted composition operator is defined by $$D_{{\varphi},u}^nf=uf^{(n)}{\circ}{\varphi},\;f{\in}H(\mathbb{D})$$. The boundedness and compactness of the generalized weighted composition operator from area Nevanlinna spaces to weighted-type spaces and little weighted-type spaces are characterized in this paper.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.125-135
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• 2014

We study the compact intertwining relations for composition operators, whose intertwining operators are Volterra type operators from the weighted Bergman spaces to the weighted Bloch spaces in the unit disk. As consequences, we find a new connection between the weighted Bergman spaces and little weighted Bloch spaces through this relations.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.217-227
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• 2020

Let ψ be an analytic function on 𝔻, the unit disc in the complex plane, and φ be an analytic self-map of 𝔻. Let 𝓑 be a Banach space of functions analytic on 𝔻. The weighted composition operator W_φ,ψ on 𝓑 is defined as W_φ,ψf = ψf ◦ φ, and the composition operator C_φ defined by C_φf = f ◦ φ for f ∈ 𝓑. Consider α > -1 and 1 ≤ p < ∞. In this paper, we prove that if φ ∈ H^∞(𝔻), then C_φ has closed range on any weighted Dirichlet space 𝒟_α if and only if φ(𝔻) satisfies the reverse Carleson condition. Also, we investigate the closed rangeness of weighted composition operators on the weighted Bergman space A^p_α.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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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.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.793-803
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• 2010

In this note, we discuss measure theoretic characterizations for weighted composition operators in some operator classes on $L^2(\cal{F})$ such as, p-quasihyponormal, p-paranormal, p-hyponormal and weakly hyponormal. Some examples are then presented to illustrate that weighted composition operators lie between these classes.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.889-896
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• 2021

Let 𝜙 be an entire self map on ℂ and let 𝜓 be an entire function on ℂ. A weighted composition operator induced by 𝜙 with weight 𝜓 is given by C_𝜓,𝜙. In this paper we investigate under what conditions the weighted composition operators C_𝜓,𝜙 on the Fock space over ℂ induced by 𝜙 with weight of the form $k_c({\zeta})=e^{{\langle}{\zeta},c{\rangle}-{\frac{{\mid}c{\mid}^2}{2}}}$ is normaloid and essentially normaloid.

• 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.60 no.5
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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.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.95-105
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• 2004

In this paper we will consider the weighted composition operators W = $uC_{\tau}$ between $L^{p}$$(X,\sum,\mu$) spaces and Orlicz spaces $L^{\phi}$$(X,\sum,\mu$) generated by measurable and non-singular transformations $\tau$ from X into itself and measurable functions u on X. We characterize the functions u and transformations $\tau$ that induce weighted composition operators between $L^{p}$ -spaces by using some properties of conditional expectation operator, pair (u,${\gamma}$) and the measure space $(X,\sum,\mu$). Also, some other properties of these types of operators will be investigated.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.583-591
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• 2003

For a weighted composition operator $uC_{\varphi}$ on C(X), we determine its essential norm and the constant for its Hyers-Ulam stability, in terms of the set $\varphi(\{x\;\in\;X\;:\;$\mid$u(x)$\mid$\;\geq\;r\})$ (r > 0).