• 대한수학회보
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• 제44권3호
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• pp.475-482
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• 2007

In this paper, we study composition operators $C_{\varph}f=f^{\circ}{\varph}$, induced by a fixed analytic self-map of the of the upper half-plane, acting between Hardy and Bloch-type spaces of the upper half-plane.

• 대한수학회보
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• 제55권4호
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• pp.1137-1147
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• 2018

In this paper, we discovered a sufficient condition ensuring the weighted composition operators $C_{{\omega}_1,{\varphi}_1},{\cdots},C_{{\omega}_N,{\varphi}_N}$ were disjoint supercyclic on $H({\Omega})$ endowed with the compact open topology. Besides, we provided a condition on inducing symbols to guarantee the disjoint supercyclicity of non-constant adjoint multipliers $M^*_{{\varphi}_1},M^*_{{\varphi}_2},{\cdots},M^*_{{\varphi}_N}$ on a Hilbert space ${\mathcal{H}}$.

• 대한수학회보
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• 제52권3호
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• pp.751-759
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• 2015

In this paper, we give new characterizations of the boundedness and compactness of composition operators $C_{\varphi}$ between Bloch type spaces in the unit ball $\mathbb{B}^n$, in terms of the power of the components of ${\varphi}$, where ${\varphi}$ is a holomorphic self-map of $\mathbb{B}^n$.

• 대한수학회논문집
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• 제22권3호
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• pp.373-382
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• 2007

In this paper, we characterize the boundedness and compactness of weighted composition operators ${\psi}C{\varphi}f=\psi(f^{\circ}\varphi)$ acting between Bergman and Bloch spaces of holomorphic functions on the open unit disk D.

• 대한수학회보
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• 제52권5호
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• pp.1711-1719
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• 2015

We obtain a new criterion for the boundedness and compactness of the weighted composition operators ${\psi}C_{\varphi}$ from ${\ss}^{{\alpha}}$(0 < ${\alpha}$ < 1) to ${\ss}^{{\beta}}$ in terms of the sequence $\{{\psi}{\varphi}^n\}$. An estimate for the essential norm of ${\psi}C_{\varphi}$ is also given.

• 대한수학회보
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• 제55권2호
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• pp.507-514
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• 2018

Let $\{{\varphi}_n\}_{n{\geq}1}$ be a sequence of analytic self-maps of ${\mathbb{D}}$. It is proved that if the union set of the ranges of the composition operators $C_{{\varphi}_n}$ on the weighted Bergman spaces contains the disk algebra, then ${\varphi}_k$ is an automorphism of ${\mathbb{D}}$ for some $k{\geq}1$.

• 호남수학학술지
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• 제46권1호
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• pp.60-69
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• 2024

We consider a special orthonormal basis for the Hardy space of the unit disc to compute the matrix representations of the composition operators with respect to the basis particulary associated to two symbols which are the inverse and the origin symmetry of the Riemann self map in the unit disc, and then we find a certain symmetry of the matrices.

• 대한수학회보
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• 제47권3호
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• pp.623-632
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• 2010

A holomorphic function F defined on the unit disc belongs to $A^{p,{\alpha}}$ (0 < p < $\infty$, 1 < ${\alpha}$ < $\infty$) if $\int\limits_U|F(z)|^p \frac{1}{1-|z|}(1+log)\frac{1}{1-|z|})^{-\alpha}$ dxdy < $\infty$. For boundedness of the composition operator defined by $C_{fg}=g{\circ}f$ mapping Blochs into $A^{p,{\alpha}$ the following (1) is a sufficient condition while (2) is a necessary condition. (1) $\int\limits_o^1\frac{1}{1-r}(1+log\frac{1}{1-r})^{-\alpha}M_p(r,\lambda{\circ}f)^p\;dr$ < $\infty$ (2) $\int\limits_o^1\frac{1}{1-r}(1+log\frac{1}{1-r})^{-\alpha+p}(1-r)^pM_p(r,f^#)^p\;dr$ < $\infty$.

• Korean Journal of Mathematics
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• 제24권4호
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• pp.647-662
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• 2016

In this paper, we study Lipschitz continuous, the boundedness and compactness of the composition operator $C_{\phi}$ acting between the general hyperbolic Bloch type-classes ${\mathcal{B}}^{\ast}_{p,{\log},{\alpha}}$ and general hyperbolic Besov-type classes $F^{\ast}_{p,{\log}}(p,q,s)$. Moreover, these classes are shown to be complete metric spaces with respect to the corresponding metrics.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권1호
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• pp.1-20
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• 2018

Service composition in the Inter-Cloud raises new challenges that are caused by the different Quality of Service (QoS) requirements of the users, which are served by different geo-distributed Cloud providers. This paper aims to explore how to select and compose such services while considering how to reach high efficiency on cost and response time, low network latency, and high reliability across multiple Cloud providers. A new hybrid multi-objective evolutionary algorithm to perform the above task called LS-NSGA-II-DE is proposed, in which the differential evolution (DE) algorithm uses the adaptive mutation operator and crossover operator to replace the those of the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to get the better convergence and diversity. At the same time, a Local Search (LS) method is performed for the Non-dominated solution set F{1} in each generation to improve the distribution of the F{1}. The simulation results show that our proposed algorithm performs well in terms of the solution distribution and convergence, and in addition, the optimality ability and scalability are better compared with those of the other algorithms.