• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1255-1268
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• 2022

We consider the Schrödinger type operator 𝓛 = (-𝚫_ℍⁿ)² + V² on the Heisenberg group ℍⁿ, where 𝚫_ℍⁿ is the sub-Laplacian and the non-negative potential V belongs to the reverse Hölder class RH_s for s ≥ Q/2 and Q ≥ 6. We shall establish the (L^p, L^q) estimates for the Riesz transforms T_𝛼,𝛽,j = V^2𝛼𝛁^j_ℍⁿ𝓛^-𝛽, j = 0, 1, 2, 3, where 𝛁_ℍⁿ is the gradient operator on ℍⁿ, 0 < α ≤ 1-j/4, j/4 < 𝛽 ≤ 1, and 𝛽 - 𝛼 ≥ j/4.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.523-537
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• 2019

We estimate the essential norms of Volterra-type integral operators $V_g$ and $I_g$, and multiplication operators $M_g$ with holomorphic symbols g on a large class of generalized Fock spaces on the complex plane ${\mathbb{C}}$. The weights defining these spaces are radial and subjected to a mild smoothness conditions. In addition, we assume that the weights decay faster than the classical Gaussian weight. Our main result estimates the essential norms of $V_g$ in terms of an asymptotic upper bound of a quantity involving the inducing symbol g and the weight function, while the essential norms of $M_g$ and $I_g$ are shown to be comparable to their operator norms. As a means to prove our main results, we first characterized the compact composition operators acting on the spaces which is interest of its own.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.899-908
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• 2017

We call a sequence $(T_n)_n$ of bounded operators on a Banach space X, BSC-Sequence if it is a Cauchy sequence in the strong operator topology and is uniformly bounded below. We determine conditions under which such sequences has a fixed point.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.743-750
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• 2009

A class of Hermitian operators B admitting a positive semidefinite solution of the linear operator equation ${\sum}^n_{j=1}A^{n-j}XA^{j-1}=B$ for a fixed positive definite operator A is given via the Furuta inequality.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.671-694
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• 2018

In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\;{\mathbb{R}}^n,\;w_1){\times}{\cdots}{\times}L^{p_m}(l^{q_m};\;{\mathbb{R}}^n,\;w_m)$ to $L^p(l^q;\;{\mathbb{R}}^n,\;{\nu}_{\vec{w}})$, with $p_1,{\cdots},p_m$, $q_1,{\cdots},q_m{\in}(1,\;{\infty})$, $1/p=1/p_1+{\cdots}+1/p_m$, $1/q=1/q_1+{\cdots}+1/q_m$ and ${\vec{w}}=(w_1,{\cdots},w_m)$ a multiple $A_{\vec{P}}$ weights. Our argument also leads to the weighted weak type endpoint estimates for the commutators. As applications, we obtain some new weighted estimates for the $Calder{\acute{o}}n$ commutator.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.109-118
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• 2015

In the present paper, a new analytic function valued integral operator is introduced which is defined on n-copies of a subset of the class of normalized analytic functions on the unit disc of the complex plane. This operator, which is denoted here by $\mathfrak{J}^{{\alpha}_i,{\beta}_i}(f_1,{\ldots},f_n)$, unifies and generalizes several integral operators studied earlier. Interesting sufficient conditions are derived for the univalent starlikeness of $\mathfrak{J}^{{\alpha}_i,{\beta}_i}(f_1,{\ldots},f_n)$.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1801-1816
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• 2017

We study some spectral properties of Volterra-type integral operators $V_g$ and $I_g$ with holomorphic symbol g on the Fock-Sobolev spaces ${\mathcal{F}}^p_{{\psi}m}$. We showed that $V_g$ is bounded on ${\mathcal{F}}^p_{{\psi}m}$ if and only if g is a complex polynomial of degree not exceeding two, while compactness of $V_g$ is described by degree of g being not bigger than one. We also identified all those positive numbers p for which the operator $V_g$ belongs to the Schatten $S_p$ classes. Finally, we characterize the spectrum of $V_g$ in terms of a closed disk of radius twice the coefficient of the highest degree term in a polynomial expansion of g.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.5
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• pp.412-418
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• 2011

The scale of wind turbines has continuously increased over the last decade. Especially, the rapid growth of the rotor diameter has brought about the increase of the tower height and the load on the rotor blade, as can be seen in the case of a 5MW class wind turbine with 126m rotor diameter. This trend means the increasing possibility of system failure. In addition to that, it is impossible for human operators to stay and manage all the turbines in the case of a large-scale wind farm. For these reasons, the operation and maintenance technology is getting more importance. In this paper, we present an unmanned remote monitoring system for MW class wind turbines and its application to YeungHeung wind test bed.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.893-913
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• 2020

Let 𝓢 be the collection of the operator matrices $\(\array{A&C\\Z&B}\)$ where the range of C is closed. In this paper, we study the properties of operator matrices in the class 𝓢. We first explore various local spectral relations, that is, the property (β), decomposable, and the property (C) between the operator matrices in the class 𝓢 and their component operators. Moreover, we investigate Weyl and Browder type spectra of operator matrices in the class 𝓢, and as some applications, we provide the conditions for such operator matrices to satisfy a-Weyl's theorem and a-Browder's theorem, respectively.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.269-276
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• 2002

Let E be a real Banach space. Let T : E longrightarrow E be a map with F(T) : = { x $\in$ E : Tx = x} $\neq$ 0 and satisfying the accretive-type condition $\lambda\$\mid$x-Tx\$\mid$^2$, for all $x\inE,\;x^*\inf(T)\;and\;\lambda >0$. We prove some necessary and sufficient conditions for the convergence of the Mann iterative sequence to a fixed point of T.