• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.425-437
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• 2002

Let $\Omega$ be a smoothly bounded pseudoconvex domain in $C^{n}$ and let $z^{0}$ $\in$b$\Omega$ a point of finite type. We also assume that the Levi form of b$\Omega$ is comparable in a neighborhood of $z^{0}$ . Then we get precise estimates of the Bergman kernel function, $K_{\Omega}$(z, w), and its derivatives in a neighborhood of $z^{0}$ . .

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.349-355
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• 1995

Let $D \subset C^n$ be a smoothly bounded pseudoconvex domain and let ${\bar{D}_r}_r$ be a family of smooth perturbations of $\bar{D}$ such that $\bar{D} \subset \bar{D}_r$. Let $K_D(z, w)$ be the Bergman kernel function on $D \times D$. Then $lim_{r \to 0} K_{D_r}(z, w) = K_D(z, w)$ locally uniformally on $D \times D$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1551-1567
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• 2019

In this paper, Seiberg-Witten-like equations are written down on 3-manifolds. Then, it has been proved that the $L^2$-solutions of these equations are trivial on ${\mathbb{R}}^3$. Finally, a global solution is obtained on the strictly pseudoconvex CR-3 manifolds for a given constant negative scalar curvature.

• Communications of the Korean Mathematical Society
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• v.3 no.1
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• pp.85-91
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• 1988

• East Asian mathematical journal
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• v.6 no.1
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• pp.101-110
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• 1990

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.85-92
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• 1995

• East Asian mathematical journal
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• v.11 no.2
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• pp.125-131
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• 1995

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1241-1249
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• 2020

Let Ω be a domain in ℂⁿ. Suppose that ∂Ω is smooth pseudoconvex of D'Angelo finite type near a boundary point ξ₀ ∈ ∂Ω and the Levi form has corank at most 1 at ξ₀. Our goal is to show that if the squeezing function s_Ω(𝜂_j) tends to 1 or the Fridman invariant h_Ω(𝜂_j) tends to 0 for some sequence {𝜂_j} ⊂ Ω converging to ξ₀, then this point must be strongly pseudoconvex.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.321-338
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• 2008

Let $\bar{M}$ be a smoothly bounded pseudoconvex complex manifold with a family of almost complex structures $\{L^{\tau}\}_{{\tau}{\in}I}$, $0{\in}I$, which extend smoothly up to bM, the boundary of M, and assume that there is ${\lambda}{\in}C^{\infty}$(bM) which is strictly subharmonic with respect to the structure $L^0|_{bM}$ in any direction where the Levi-form vanishes on bM. We obtain explicit estimates for the $\bar{\partial}$-Neumann problem in Sobolev spaces both in space and parameter variables. Also we get a similar result when $\bar{M}$ is strongly pseudoconvex.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.339-350
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• 2005

We obtain the following two inequalities on a strongly pseudoconvex domain $\Omega\;in\;\mathbb{C}^n\;:\;for\;f\;{\in}\;O(\Omega)$ $$\int_{0}^{{\delta}0}t^{a{\mid}a{\mid}+b}M_p^a(t, D^{a}f)dt\lesssim\int_{0}^{{\delta}0}t^{b}M_p^a(t,\;f)dt\;\int_{O}^{{\delta}O}t_{b}M_p^a(t,\;f)dt\lesssim\sum_{j=0}^{m}\int_{O}^{{\delta}O}t^{am+b}M_{p}^{a}\(t,\;\aleph^{i}f\)dt$$. In [9], Shi proved these results for the unit ball in $\mathbb{C}^n$. These are generalizations of some classical results of Hardy and Littlewood.