• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1229-1236
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• 2009

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator S$_K$ on a vector-valued Hardy space H$^2$(${\Omega}$, K) is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions and quasi-inner divisors.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.137-160
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• 2006

We describe the weight functions for which Hardy's inequality of nonincreasing functions is satisfied. Further we characterize the pairs of weight functions $(w,v)$ for which the Laplace transform $\mathcal{L}f(x)={\int}^{\infty}_0e^{-xy}f(y)dy$, with monotone function $f$, is bounded from the weighted Lebesgue space $L^p(w)$ to $L^q(v)$.

• 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.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.397-410
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• 2002

In this paper, some inequalities for vector-valued maximal functions over locally compact Vienkin groups are obtained.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.435-452
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• 2004

In this paper, we prove the weighted continuity of multilinear Marcinkiewicz operators for the extreme cases of p.

• East Asian mathematical journal
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• v.16 no.2
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• pp.169-174
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• 2000

We give an easy proof that ${\phi}(z)=\frac{z^2_1}{1-z^2_2}$ induces the bounded composition operator $C_{\phi}:\mathcal{B}{\rightarrow}{\bigcap}H^p(B_2)$ defined by $C_{\phi}f=f\;o\;{\phi}$.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.139-151
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• 2012

In the previous paper, we gave a characterization of backward shift invariant subspaces of the Hardy space over the bidisk on which [${S_z}^n$, $S_w^*$] = 0 for a positive integer n ${\geq}$ 2. In this case, it holds that ${S_z}^n=cI$ for some $c{\in}\mathbb{C}$. In this paper, it is proved that if [$S_{\varphi}$, $S_w^*$] = 0 and ${\varphi}{\in}H^{\infty}({\Gamma}_z)$, then $S_{\varphi}=cI$ for some $c{\in}\mathbb{C}$.

• Journal of Korean Tunnelling and Underground Space Association
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• v.18 no.3
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• pp.291-303
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• 2016

Recently, various forms of diverging sections in tunnels have been designed as the demand for underground passageway in urban areas increases. Therefore, the complexity of the ventilation system in tunnels with diverging sections requires a ventilation analysis method different from the conventional method for the straight tunnels. None of the domestic and foreign tunnel ventilation design standards specifies the method for the ventilation network analysis, and the numerical analysis methods have been most widely used. This paper aims at reviewing the ventilation network analytical method applicable as the design standard. The proposed method is based on the characteristic equations rather than the numerical analysis. Thanks to the advantages of easy application, the Hardy-Cross method has been widely applied in the fields of mine ventilation and tunnel ventilation. However, limitations with the cutting errors in the Taylor series expansion and the convergence problem mainly caused by the mesh selection algorithm have been reported. Therefore, this paper examines the applicability of the ventilation analysis method for network-type tunnels with the gradient method that can analyze flow rate and pressure simultaneously without the configuration of mesh. A simple ventilation analysis method for network-type tunnels is proposed.

• 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 $H^2$.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.931-940
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• 2007

Holomorphic mean Lipschitz space is defined in the unit ball of $\mathbb{C}^n$. The membership of the space is expressed in terms of the growth of radial derivatives, which reduced to a classical result of Hardy and Littlewood when n = 1. The membership is also expressed in terms of the growth of tangential derivatives when $n{\ge}2$.