• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.235-251
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• 2021

We consider the Schrödinger type operator ��k = (-∆)k+Vk on ℝn(n ≥ 2k + 1), where k = 1, 2 and the nonnegative potential V belongs to the reverse Hölder class RHs with n/2 < s < n. In this paper, we establish the (Lp, Lq)-boundedness of the higher order Riesz transform T��,�� = V2��∇2��-��2 (0 ≤ �� ≤ 1/2 < �� ≤ 1, �� - �� ≥ 1/2) and its adjoint operator T∗��,�� respectively. We show that T��,�� is bounded from Hardy type space $H^1_{\mathcal{L}_2}({\mathbb{R}}_n)$ into Lp2 (ℝn) and T∗��,�� is bounded from ��p1 (ℝn) into BMO type space $BMO_{\mathcal{L}_1}$ (ℝn) when �� - �� > 1/2, where $p_1={\frac{n}{4({\beta}-{\alpha})-2}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})+2}}$. Moreover, we prove that T��,�� is bounded from $BMO_{\mathcal{L}_1}({\mathbb{R}}_n)$ to itself when �� - �� = 1/2.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.161-170
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• 2022

It is presented a Banach space of functions of bounded mean oscillation BMO type.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.141-146
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• 1997

In this paper we prove that the corona theorem for the algebra $H^{\infty}(D){\cap}D(D)$. That is, we prove that $\mathcal{M}{\setminus}{\overline{D}}$ is an empty set where $\mathcal{M}$ is the maximal ideal space of the given algebra.

• Journal of Life Science
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• v.9 no.2
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• pp.176-181
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• 1999

In order to understand molecular phylogenetics of silkworm (Bombyx mori), we analyzed the sequences of BmoMAR isolated from Bomhyx mori that is partial coding gene of transposase of mariner-like element(MLE). By pairwise comparing nucleotide sequences of BmoMAR with ten previously reported insect MLEs accessed in GeneBank, the average genetic distance was estimated to be 0.4840. The phylogenetics tree constructed from nine insect species except for human MLE(Hsmarl) by UPGMA method indicated that MLEs are divided into three clusters, and Drosophila mariutiana was independently subgrouped. Bombyx mori(BmoMAR) was subgrouped with microcaddishfly (Orthotrichia cristata), webworm(Atteva punctella), almond moth(Ephestia cautella), Hyalopora cecropia which we lepidoptera. Phylogenetics tree according to UPGMA principle, on the basis of informative nucleotide sequences of nine insect MLEs, indicated that Bombyx mori was more closely related to microcaddishfly(Orthotrichia cristata) and webworm (Atteva punctella) of lepidoptera. We suggest that insect MLEs are a useful key for studying molecular phylogenetics among intra species of insects.

• Convergence Security Journal
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• v.13 no.3
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• pp.71-77
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• 2013

In our country security industry biz model analysis methodology fragmentary theory exists, but it is hard to find a comprehensive analysis methodology. Biz model analysis IT companies the external factors and internal factors to integrate the information gathered about the comprehensive analysis of the development of an information system are required. Information support system early in the software architecture of the system design decisions early decision as the design, development, testing, maintenance, has a lasting impact on the project as a guideline in the development of a framework of design abstraction. BMO evaluation support information systems architecture designs system purposes. The mission must support the execution. Information system stakeholders to determine the mission and the environment. All information systems architecture shall have architecture. Technology architecture should be documented with each other can be used. Determine the architecture based architecture descriptions are presented.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1087-1100
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• 2005

In this note we give the mapping properties of the Marcinkiewicz integral !-to. at some end spaces. More precisely, we first prove that !-to. is a bounded operator from H$^{1,($\mathbb{R) to H$^{1, ($\mathbb{R). As a corollary of the results above, we obtain again the weak type (1,1) boundedness of $\mu$$_{, but the condition assumed on n is weaker than Stein's condition. Finally, we show that !-to. is bounded from BMO($\mathbb{R) to BMO($\mathbb{R). The results in this note are the extensions of the results obtained by Lee and Rim recently.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1117-1127
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• 2019

Let ${\mathcal{L}}_2=(-{\Delta})^2+V^2$ be the $Schr{\ddot{o}}dinger$ type operator, where nonnegative potential V belongs to the reverse $H{\ddot{o}}lder$ class $RH_s$, s > n/2. In this paper, we consider the operator $T_{{\alpha},{\beta}}=V^{2{\alpha}}{\mathcal{L}}^{-{\beta}}_2$ and its conjugate $T^*_{{\alpha},{\beta}}$, where $0<{\alpha}{\leq}{\beta}{\leq}1$. We establish the $(L^p,\;L^q)$-boundedness of operator $T_{{\alpha},{\beta}}$ and $T^*_{{\alpha},{\beta}}$, respectively, we also show that $T_{{\alpha},{\beta}}$ is bounded from Hardy type space $H^1_{L_2}({\mathbb{R}}^n)$ into $L^{p_2}({\mathbb{R}}^n)$ and $T^*_{{\alpha},{\beta}}$ is bounded from $L^{p_1}({\mathbb{R}}^n)$ into BMO type space $BMO_{{\mathcal{L}}1}({\mathbb{R}}^n)$, where $p_1={\frac{n}{4({\beta}-{\alpha})}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})}}$.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.495-517
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• 2022

Let M_α be a bilinear fractional maximal operator and BM_α be a fractional maximal operator associated with the bilinear Hilbert transform. In this paper, the compactness on weighted Lebesgue spaces are considered for commutators of bilinear fractional maximal operators; these commutators include the fractional maximal linear commutators M^j_α,β and BM^j_α,β (j = 1, 2), the fractional maximal iterated commutator ${\mathcal{M}}_{{\alpha},{\vec{b}}}$, and $BM_{{\alpha},{\vec{b}}}$, where b ∈ BMO(ℝ^d) and ${\vec{b}}\;=\;(b_1,b_2)\;{\in}\;BMO({\mathbb{R}}^d)\;{\times}\;BMO({\mathbb{R}}^d)$. In particular, we improve the well-known results to a larger scale for 1/2 < q < ∞ and give positive answers to the questions in [2].

• Asia-Pacific Journal of Business Venturing and Entrepreneurship
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• v.2 no.2
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• pp.49-68
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• 2007

This paper develop self pre-checkup lists for the validity of business model as web business starters can utilize to open business. In particular, self pre-checkup lists invented by Dr. Bruce Merrifield, is reapplied and modified in appropriate to internet shopping mall business. This paper complete many literature reviews to identify appropriate factors of evaluation such as about the characters of internet business, business validity testing theory for internet business model, pros and cons of e-business and startup ventures, factor analysis of technology valuation, and pros and cons for internet shopping mall. This paper define six different factors; scale of sales, the growth rate of market, competitiveness, risk portfolio, industry upside down, and social conditions, as the factors of evaluating the business attractiveness. Meanwhile, it define characters of CEO, content's power, mutual inclusion, commerce, fulfillment, marketing power as the factors of business appropriateness. This paper also conducts several case studies; company I, D, G of applying the former model. This paper sort out internet business model in imaginations by utilizing self pre-checkup lists of business evaluation. Also, the outcomes of evaluation is expected to provide meaningful future business implications.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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• pp.1273-1299
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• 2012

We prove the global regularity of weak solutions to a conormal derivative boundary value problem for quasilinear elliptic equations in divergence form on Lipschitz domains under the controlled growth conditions on the low order terms. The leading coefficients are in the class of BMO functions with small mean oscillations.