• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.469-479
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• 2003

Let B be the open unit ball in $C^{n}$ and ${\mu}_{q}$(q > -1) the Lebesgue measure such that ${\mu}_{q}$(B) ＝ 1. Let ${L_{a,q}}^2$ be the subspace of ${L^2(B,D{\mu}_q)$ consisting of analytic functions, and let $\overline{{L_{a,q}}^2}$ be the subspace of ${L^2(B,D{\mu}_q)$) consisting of conjugate analytic functions. Let $\bar{P}$ be the orthogonal projection from ${L^2(B,D{\mu}_q)$ into $\overline{{L_{a,q}}^2}$. The little Hankel operator ${h_{\varphi}}^{q}\;:\;{L_{a,q}}^2\;{\rightarrow}\;{\overline}{{L_{a,q}}^2}$ is defined by ${h_{\varphi}}^{q}(\cdot)\;=\;{\bar{P}}({\varphi}{\cdot})$. In this paper, we will find the necessary and sufficient condition that the little Hankel operator ${h_{\varphi}}^{q}$ is bounded(or compact).

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.63-78
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• 2008

We generalize several integral inequalities for analytic functions on the open unit polydisc $U^n={\{}z{\in}C^n||zj|<1,\;j=1,...,n{\}}$. It is shown that if a holomorphic function on $U^n$ belongs to the mixed norm space $A_{\vec{\omega}}^{p,q}(U^n)$, where ${\omega}_j(\cdot)$,j=1,...,n, are admissible weights, then all weighted derivations of order $|k|$ (with positive orders of derivations) belong to a related mixed norm space. The converse of the result is proved when, p, q ${\in}\;[1,\;{\infty})$ and when the order is equal to one. The equivalence of these conditions is given for all p, q ${\in}\;(0,\;{\infty})$ if ${\omega}_j(z_j)=(1-|z_j|^2)^{{\alpha}j},\;{\alpha}_j>-1$, j=1,...,n (the classical weights.) The main results here improve our results in Z. Anal. Anwendungen 23 (3) (2004), no. 3, 577-587 and Z. Anal. Anwendungen 23 (2004), no. 4, 775-782.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.885-898
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• 2019

This paper gives a counterexample to show that the first order commutator $C_2$ is not bounded from $H^1({\mathbb{R}}){\times}H^1({\mathbb{R}})$ into $L^{1/2}({\mathbb{R}})$. Then we introduce the atomic definition of abstract weighted Hardy spaces $H^1_{ato,{\omega}}$$({\mathbb{R}})$ and study its properties. At last, we prove that $C_2$ maps $H^1_{ato,{\omega}}$$({\mathbb{R}}){\times}H^1_{ato,{\omega}}$$({\mathbb{R}})$ into $L^{1/2}_{\omega}$$({\mathbb{R}})$.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.879-895
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• 2022

This paper establishes the Baum-Katz type theorem and the Marcinkiewicz-Zymund type strong law of large numbers for sequences of coordinatewise negatively associated and identically distributed random vectors {X, X_n, n ≥ 1} taking values in a Hilbert space H with general normalizing constants $b_n=n^{\alpha}{\tilde{L}}(n^{\alpha})$, where ${\tilde{L}}({\cdot})$ is the de Bruijn conjugate of a slowly varying function L(·). The main result extends and unifies many results in the literature. The sharpness of the result is illustrated by two examples.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.313-326
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• 2018

The paper studies some new ${\mathbb{C}}^n$-generalizations of Bergman type operators introduced by Shields and Williams depending on a normal pair of weight functions. We find the values of parameter ${\beta}$ for which these operators are bounded on mixed norm spaces L(p, q, ${\beta}$) over the unit ball in ${\mathbb{C}}^n$. Moreover, these operators are bounded projections as well, and the images of L(p, q, ${\beta}$) under the projections are found.

• International Journal of High-Rise Buildings
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• v.7 no.2
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• pp.171-183
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• 2018

Turner and Penn (1) from UCL have proved that Visibility Graph Analysis (VGA) can be used as a more accurate method to predict the pedestrian distribution in building spaces. However, this methodology neglects certain elements that are of special influence on pedestrian distribution in buildings, especially the entrances and exits. Based on Space Syntax, this dissertation improves on the traditional method of Visibility Graph Analysis, using three shopping centers in Shenzhen as examples, attempts to explore a new parameter - "attenuation index of pedestrians at the entrances and exits" - using relevant data of the entrances and exits of the three cases, and combines it with traditional VGA analysis through weighted calculation, in order to provide more accurate predictions of pedestrian patterns in shopping centers.

• Restorative Dentistry and Endodontics
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• v.6 no.1
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• pp.133-139
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• 1980

In this experiment, etching was performed on the incisor enamel surfaces of 13 Albino rats, weighted about 130gm, with both 30% and 50% concentrations of the phosphoric, citric acids, and EDTA solution for 60 seconds. Immediately after extraction of the animal teeth, laboratory procedures for scanning electron microscopic observations were made and the author derived the following conclusions: 1. On the enamel surface treated with 30% and 50% phosphoric acids, all of the periphery, center of the enamel rods, and the enamel matrices were severely etched. 2. In the etched with 30% citric acid group, only the small part of the enamel rods were etched out. In case of 50% citric acid the periphery, center of enamel rods were partially or entirely etched, and the intermatrix spaces were widened. 3. In the 30% and 50% of the EDTA etched groups, the periphery of the enamel rods explicitely were etched, and the spaces between matrices were widened.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.745-756
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• 2019

We obtain Lipschitz type characterization and double integral characterization for Fock-type spaces with the norm $${\parallel}f{\parallel}^p_{F^p_{m,{\alpha},t}}\;=\;{\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{C}}^n}}\;{\left|{f(z){e^{-{\alpha}}{\mid}z{\mid}^m}}\right|^p}\;{\frac{dV(z)}{(1+{\mid}z{\mid})^t}}$$, where ${\alpha}>0$, $t{\in}{\mathbb{R}}$, and $m{\in}\mathbb{N}$. The results of this paper are the extensions of the classical weighted Fock space $F^p_{2,{\alpha},t}$.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1359-1380
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• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.

• Honam Mathematical Journal
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• v.35 no.3
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• pp.343-350
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• 2013

In this paper we prove that if Toeplitz operators $T^{\alpha}_u$ with symbols in RW satisfy ${\parallel}uk^{\alpha}_z{\parallel}_{s,{\alpha}{\rightarrow}0$ as $z{\rightarrow}{\partial}\mathbb{D}$ then $T^{\alpha}_u$ is compact and also prove that if $T^{\alpha}_u$ is compact then the Berezin transform of $T^{\alpha}_u$ equals to zero on ${\partial}\mathbb{D}$.