• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.369-378
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• 2005

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

• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.465-474
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• 2006

In this paper, we characterize the boundedness and compactness of weighted composition operators ${\psi}C_{\varphi}f={\psi}fo{\psi}$ acting between Bergman-type spaces.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1785-1794
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• 2016

This paper gives complete characterization for isometric weighted composition operators on the Fock space of ${\mathbb{C}}^N$. The main result shows that an isometric weighted composition operator on the Fock space of ${\mathbb{C}}^N$ is a unitary operator.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.719-727
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• 2006

In this paper, we study the boundedness and the com-pactness of weighted composition operator between $H^{\infty}$ and Bergman type space on the unit ball of $\mathbb{C}^n$. Also, the norm of corresponding weighted composition operator is computed.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.63-70
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• 2005

In this paper we study bounded and compact weighted composition operator, induced by a fixed analytic function and an analytic self-map of the open unit disk, from Bergman space into weighted Bloch space. As a corollary, obtain the characterization of composition operator from Bergman space into weighted Bloch space.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.527-540
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• 2010

We characterize the boundedness and compactness of the weighted composition operator on the logarithmic Bloch space $\mathcal{L}\ss=\{f{\in}H(D):sup_D(1-|z|^2)ln(\frac{2}{1-|z|})|f'(z)|$<+$\infty$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$. The results generalize the known corresponding results on the composition operator and the pointwise multiplier on the logarithmic Bloch space ${\mathcal{L}\ss$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1119-1124
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• 2011

In the present paper, we study the chaotic property of weighted composition operators acting on the holomorphic function space $H(\mathbb{U})$.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1119-1129
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• 2022

We formulate the matrix representation of a composition operator on the Hardy space of the unit disc with the symbol which is a Riemann map of the unit disc, with respect to a special orthonormal basis.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.599-612
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• 2017

If ${\psi}$ is analytic on the open unit disk $\mathbb{D}$ and ${\varphi}$ is an analytic self-map of $\mathbb{D}$, the weighted composition operator $C_{{\psi},{\varphi}}$ is defined by $C_{{\psi},{\varphi}}f(z)={\psi}(z)f({\varphi}(z))$, when f is analytic on $\mathbb{D}$. In this paper, we study normal, cohyponormal, hyponormal and normaloid weighted composition operators on the Hardy and weighted Bergman spaces. First, for some weighted Hardy spaces $H^2({\beta})$, we prove that if $C_{{\psi},{\varphi}}$ is cohyponormal on $H^2({\beta})$, then ${\psi}$ never vanishes on $\mathbb{D}$ and ${\varphi}$ is univalent, when ${\psi}{\not\equiv}0$ and ${\varphi}$ is not a constant function. Moreover, for ${\psi}=K_a$, where |a| < 1, we investigate normal, cohyponormal and hyponormal weighted composition operators $C_{{\psi},{\varphi}}$. After that, for ${\varphi}$ which is a hyperbolic or parabolic automorphism, we characterize all normal weighted composition operators $C_{{\psi},{\varphi}}$, when ${\psi}{\not\equiv}0$ and ${\psi}$ is analytic on $\bar{\mathbb{D}}$. Finally, we find all normal weighted composition operators which are bounded below.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.507-513
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• 2018

We will consider the asymptotic toeplitzness associated with weighted composition operators on the Hardy-Hilbert space $H^2$.