• Honam Mathematical Journal
• /
• v.39 no.2
• /
• pp.143-159
• /
• 2017

In this paper, we show that algebraic properties of Toeplitz operators on both Bergman spaces and Hardy spaces on the unit disc essentially generalizes on arbitrary bounded domains in the plane. In particular, we obtain results for the uniqueness property and commuting problems of the Toeplitz operators on the Hardy and the Bergman spaces associated to bounded domains.

• Communications of the Korean Mathematical Society
• /
• v.24 no.1
• /
• pp.57-66
• /
• 2009

In this paper, we characterize the boundedness and compactness of the extended $Ces{\grave{a}}ro$ operators from general function spaces F(p, q, s) to Bloch-type spaces ${\mathcal{B}}_{\mu}$ where $\mu$ is normal function on [0,1).

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.481-495
• /
• 2021

In this paper, we investigate the properties of Bergman spaces, Bloch spaces and integral means of p-harmonic functions on the unit ball in ℝn. Firstly, we offer some Lipschitz-type and double integral characterizations for Bergman space ��kγ. Secondly, we characterize Bloch space ��αω in terms of weighted Lipschitz conditions and BMO functions. Finally, a Hardy-Littlewood type theorem for integral means of p-harmonic functions is established.

• Architectural research
• /
• v.21 no.1
• /
• pp.9-20
• /
• 2019

In the spatial configuration of a unit plan, two rules exist: one that governs the arrangement of spaces, and one that controls the design process of generating a unit plan. This study defines space grammar as an integration of the two rules that give birth to a given spatial configuration and as the process of the generation of unit plans. To understand the distinctive features of Indonesian row houses, this study analyzes the unit plans of row houses in new towns of the metropolitan cities of Indonesia, derives a common space grammar from the unit plans, and interprets the sociocultural background that has produced this space grammar. This study employs Seo's (2007a; 2007b) graph-theoretic methodology to analyze the spatial configurations of unit plans along with a topographical approach to systematically illustrate the design process. The guest space was found as the most unique space of Indonesian houses, which cannot be found in other Southeast Asian houses. Kitchen was clearly seperated from the dining and living spaces, following traditional custom. Dining space was found to serve as a circulation center, connecting the entrance, the lving area and the kitchen. This study locates the basic orders of primary space and the design principles that dictate the unique spatial configurations of Indonesian row houses. This study reveals the basic space grammar that underpins the forms of Indonesian row houses, explaining the sociocultural and geo-climatic factors affecting this space grammar and proposing unique characteristics of Indonesian contemporary houses.

• Journal of the Korean housing association
• /
• v.17 no.4
• /
• pp.15-24
• /
• 2006

The purpose of this study is to unveil the characteristics of residential space organizations in dementia units. Observation, interview, and drawing analysis of the sample units were used to collect the data for new dementia unit plans. The findings revealed the lack of minimum requirement of residential spaces per person in some sample units, the necessity of consideration of group units, and the change of units based plans to each floor based plans. However, insufficient recreation rooms and the lack of caregivers' resting spaces in the sample units were uncovered. Thus, various recreation rooms such as a reading room, flower room, pottery room, bakery room, or game room should be provided in the sample units. The conclusion is that asylum oriented residential types should be changed to each floor based units having privacy and high satisfaction of residential life. The study of floor oriented residential units focusing on minimum spaces of the floor, space numbers, number of elderly persons on each floor should be studied in the near future.

• Journal of the Chungcheong Mathematical Society
• /
• v.13 no.1
• /
• pp.131-138
• /
• 2000

Let D be the open unit disk in the complex plane $\mathbb{C}$. For any q > 0, the operator $Q_q$ defined by $$Q_qf(z)=q\int_{D}\frac{f(\omega)}{(1-z{\bar{\omega}})^{1+q}}d{\omega},\;z{\in}D$$. maps $L^{\infty}(D)$ boundedly onto $B_q$ for each q > 0. In this paper, weighted Bloch spaces $\mathcal{B}_q$ (q > 0) are considered on the open unit ball in $\mathbb{C}^n$. In particular, we will investigate the possibility of extension of this operator to the Weighted Bloch spaces $\mathcal{B}_q$ in $\mathbb{C}^n$.

• Journal of the Korean Institute of Rural Architecture
• /
• v.12 no.2
• /
• pp.13-22
• /
• 2010

This study is to analyze women's power in family to be related to Anbang, kitchen, dining room, and utility room planning in a unit plan of condominium apartment housing in rural area Data were collected 194 unit plans from 9 eastern regions of Kungi-Do. The results are as followed: 1) Anbang reflects the women's power on changing its space character into mater bedroom, the highest hierarchy in private zone, and planning a dress room in it. 2) Dining room and kitchen is openly centered on the unit plan, but kitchen is still only women's working space for family and agriculture depended on literature review. Dining space is not activated family interaction, so it is not different from urban apartment housing. However, its location and character are changed, and its hierarchy is relatively higher with women. Dining room and kitchen tend to plan visually separated after 2001, so its trend seems to establish women's territory at home. 3) Whole family can't be easy to access utility and back balcony close to kitchen, and these spaces are functionally separated for women's house work. This design trend seems to establish for women's area. 4) Finally, women's power seems to be effective in house working area including kitchen space depended on results. Also, these results from rural condominium apartment are similar to urban ones in previous study.

• Communications of the Korean Mathematical Society
• /
• v.10 no.3
• /
• pp.633-642
• /
• 1995

Recently S. Axler proved that every sequence in the unit disk U converging to the boundary contains an interpolating subsequence for the multipliers of the Dirichlet space D(U). In this paper we generalizes Axler's result to the finitely connected planer domains such that the Dirichlet spaces are contained in the Bergman spaces.

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

• Journal of the Korean Mathematical Society
• /
• v.39 no.5
• /
• pp.783-800
• /
• 2002

Let B denote the unit ball in $C^n$, and ν the normalized Lebesgue measure on B. For $\alpha$ > -1, define $dv_\alpha$(z) ＝ $c_\alpha$$(1-\midz\mid^2)^{\alpha}$dν(z), z $\in$ B. Here $c_\alpha$ is a positive constant such that $v_\alpha$(B) ＝ 1. Let H(B) denote the space of all holomorphic functions in B. For $p\geq1$, define the Bergman-Privalov space $(AN)^{p}(v_\alpha)$ by $(AN)^{p}(v_\alpha)$ = ${f\inH(B)$ : $\int_B{log(1+\midf\mid)}^pdv_\alpha\;<\;\infty}$ In this paper we prove that a function $f\inH(B)$ is in $(AN)^{p}$$(v_\alpha)$ if and only if $(1+\midf\mid)^{-2}{log(1+\midf\mid)}^{p-2}\mid\nablaf\mid^2\;\epsilon\;L^1(v_\alpha)$ in the case 1＜p＜$\infty$, or $(1+\midf\mid)^{-2}\midf\mid^{-1}\mid{\nabla}f\mid^2\;\epsilon\;L^1(v_\alpha)$ in the case p ＝ 1, where $nabla$f is the gradient of f with respect to the Bergman metric on B. This is an analogous result to the characterization of the Hardy spaces by M. Stoll [18] and that of the Bergman spaces by C. Ouyang-W. Yang-R. Zhao [13].