• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.567-578
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• 2017

Many scholars studied the boundedness of $Ces{\grave{a}}ro$ operators between $Q_K$ spaces and Bloch spaces of holomorphic functions in the unit disc in the complex plane, however, they did not describe the compactness. Let 0 < ${\alpha}$ < $+{\infty}$, K(r) be right continuous nondecreasing functions on (0, $+{\infty}$) and satisfy $${\displaystyle\smashmargin{2}{\int\nolimits_0}^{\frac{1}{e}}}K({\log}{\frac{1}{r}})rdr<+{\infty}$$. Suppose g is a holomorphic function in the unit disk. In this paper, some sufficient and necessary conditions for the extended $Ces{\grave{a}}ro$ operators $T_g$ between ${\alpha}$-Bloch spaces and $Q_K$ spaces in the unit disc to be bounded and compact are obtained.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.87-101
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• 2018

The purpose of this paper is to define a new class of hyperholomorphic functions spaces, which will be called $F^{\alpha}_{{\omega},G}$(p, q, s) type spaces. For this class, we characterize hyperholomorphic weighted ${\alpha}$-Bloch functions by functions belonging to $F^{\alpha}_{{\omega},G}$(p, q, s) spaces under some mild conditions. Moreover, we give some essential properties for the extended weighted little ${\alpha}$-Bloch spaces. Also, we give the characterization for the hyperholomorphic weighted Bloch space by the integral norms of $F^{\alpha}_{{\omega},G}$(p, q, s) spaces of hyperholomorphic functions. Finally, we will give the relation between the hyperholomorphic ${\mathcal{B}}^{\alpha}_{{\omega},0}$ type spaces and the hyperholomorphic valued-functions space $F^{\alpha}_{{\omega},G}$(p, q, s).

• Journal of the Korean Institute of Rural Architecture
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• v.2 no.3
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• pp.1-14
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• 2000

This study is purposed to guide a right planning direction of public spaces in rural village. To do so, this study gives you the causes of transformation and the characteristics of the transformed public spaces in rural village. It classifies three different trends of transformed public spaces; increase, stagnation and decrease. In addition, they are related with rural population, farming types and the social consciousness. There are several characteristics of public spaces comparing before and after the transformation. Public spaces were used as small spaces, housing and farm lands before they were transformed. However, after the transformation, we could see that external spaces are augmented, public spaces are congregated and public facilities are increased.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.83-89
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• 1993

Applications of the classical Knaster-Kuratowski-Mazurkiewicz theorem [KKM] and the fixed point theory of multifunctions defined on convex subsets of topological vector spaces have been greatly improved by adopting the concept of convex spaces due to Lassonde[L]. Recently, this concept has been extended to pseudo-convex spaces, contractible spaces, or spaces having certain families of contractible subsets by Horvath[H1-4]. In the present paper we give a far-reaching generalization of the best approximation theorem of Ky Fan[F1, 2] to pseudo-metric spaces and improved versions of the well-known fixed point theorems due to Brouwer [B] and Schauder [S] for spaces having certain families of contractible subsets. Our basic tool is a generalized Fan-Browder type fixed point theorem in our previous works [P3, 4].

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.375-415
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• 2019

We study spaces of continuous-function-valued functions that have the property that composition with evaluation functionals induce $weak^*$ to norm continuous maps to ${\ell}^p$ space ($p{\in}(1,\;{\infty})$). Versions of $H{\ddot{o}}lder^{\prime}s$ inequality and Riesz representation theorem are proved to hold on these spaces. We prove a version of Dixmier's theorem for spaces of function-valued matrix operators on these spaces, and an analogue of the trace formula for operators on Hilbert spaces. When the function space is taken to be the complex field, the spaces are just the ${\ell}^p$ spaces and the well-known classical theorems follow from our results.

• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.2
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• pp.107-112
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• 2000

We will prove the existence of final smooth fuzzy topological spaces and final smooth fuzzy closure spaces. From this fact we can define quotient spaces of their spaces.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.229-248
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• 2008

The boundedness and compactness of the Volterra composition operators between weighted Bergman spaces and Bloch type spaces are discussed in this paper.

• Korean Institute of Interior Design Journal
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• v.26 no.4
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• pp.57-64
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• 2017

Modern Christian spaces are developing from the past architectural styles to the phenomenological aspects. This study was conducted since it was judged that research and analysis is desirable with the application of religious phenomenological theories which fit the characteristics of religious spaces. A scholar of religion, M. Eliade studied religious phenomenology based on religious studies. This study analyzed the characteristics of religious phenomenology of the Christian spaces based on his theory. As a research method, this study analyzed the category of religious studies and religious phenomenology derived from them and selected M. Eliade as one of the theorists in the field of religious phenomenology. Study drew out the characteristics of Christian spaces from the perspective of M. Eliade's religious phenomenology as follows; In the Christian spaces, characteristics of experiential spatiality and ambiguous spatiality appeared in relation to the spaces of 'Sacred' and 'Profane' which M. Eliade aimed to explain. The characteristics of Christian spaces drawn out from the time of 'Sacred' and 'Profane', which is M. Eliade's theory, were fundamental temporality, environmental temporality and subjective temporality. From the structure and form of 'Sacred' and 'Profane', which is M. Eliade's theory, the characteristics of Christian spaces can be considered to be formative symbolism and physical naturalness. Various characteristics of Christian spaces materialize the concepts of 'hierophany' and 'sublimity' vaguely felt in religious spaces. The results of this study is expected to provide researchers, religious people and general public who study Christian spaces with research basis to further objectify results of their studies as well as basic data on the phenomenological methodology of religion.

• Proceeding of Spring/Autumn Annual Conference of KHA
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• 2011.04a
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• pp.141-146
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• 2011

The purpose of this study is to investigate the planning of the community spaces for sustainable apartment complex under the aging society. For this, it is needed to identify the practical meaning of community spaces for elderly residents. In many cases, existing apartments' community spaces have been designed without considering the elderly. In order to develop successful environment for aging society, it is necessary for us to precisely review how elderly residents are changing their needs. Survey and depth-interview methods were used for data collection of this study. This study was performed in the five subject apartments located in Haeundae new town, Busan. In planning of community spaces for sustainable apartment complex in the aging society, 1) The population of the elderly in apartment complex has been increased with progress of the aging society, and it has been necessary to enlarge and consider the aging-friendly community space. 2) When the community space is located in a good accessibility, visual openness, multipurpose composition and the center of complex, it was investigated that the degree of its usage was high. 3) Common apartment complex for the elderly was deficient, and the composition and the layout of community spaces were needed, which included sports facility, spaces for leisure culture and study. This study could be utilized as basic data for designing community spaces in apartments from the perspective of sustainable community.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.721-745
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• 2020

In this paper we study fractional Sobolev spaces characterized by a norm based on eigenfunction expansions. The goal of this paper is twofold. The first one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 2 equipped with a norm defined in terms of Neumann eigenfunction expansions. Due to the zero Neumann trace of Neumann eigenfunctions on a boundary, fractional Sobolev spaces of order 3/2 ≤ s ≤ 2 characterized by the norm are the spaces of functions with zero Neumann trace on a boundary. The spaces equipped with the norm are useful for studying cross-sectional traces of solutions to the Helmholtz equation in waveguides with a homogeneous Neumann boundary condition. The second one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 1 for vector-valued functions in a simply-connected, bounded and smooth domain in ℝ². These spaces are defined by a norm based on series expansions in terms of eigenfunctions of the vector Laplacian with boundary conditions of zero tangential component or zero normal component. The spaces defined by the norm are important for analyzing cross-sectional traces of time-harmonic electromagnetic fields in perfectly conducting waveguides.