• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.449-457
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• 2003

On the setting of the upper half-space of the Euclidean space $R^{n}$, we show that to each weighted harmonic Bergman function $u\;\epsilon\;b^p_{\alpha}$, there corresponds a unique conjugate system ($upsilon$_1,…, $upsilon_{n-1}$) of u satisfying $upsilon_j{\epsilon}\;b^p_{\alpha}$ with an appropriate norm bound.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.127-134
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• 2000

Let $\Omega$ be a bounded pseudoconvex domain in$C^{n}$ with smooth defining function r and let$z_0\; {\in}\; b{\Omega}$ be a point of finite type. We also assume that $\Omega$ is convex in a neighborhood of $z_0$. Then we prove that all the holomorphic sectional curvatures of the Bergman metric of $\Omega$ are bounded below by a negative constant near $z_0$.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.661-678
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• 1995

In this paper we will estimate from above and below the values of the Bergman, Caratheodory and Kobayashi metrics for a vector X at z, where z is any point near a given point $z_0$ in the boundary of pseudoconvex domains in $C^n$.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1483-1490
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• 2018

In this note, it is proven that the slice Bergman kernels for some axially symmetric slice domains are zero-free by a simple method.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.387-396
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• 2005

In the setting of the half-plane of the complex plane, we introduce a modified reproducing kernel and we show that for $r>-1/2,\;B^{1,r}-cancellation$ property holds and the Bloch space is the dual space of $B^{1,r}$.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.413-424
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• 2023

The main purpose of this paper is to show that over a large class of bounded domains Ω ⊂ ℂ², for 1 < p < ∞, the Bergman projection 𝓟 is bounded from L^p(Ω, dV ) to the Bergman space A^p(Ω); from L^∞(Ω) to the holomorphic Bloch space BlHol(Ω); and from L¹(Ω, P(z, z)dV) to the holomorphic Besov space Besov(Ω), where P(ζ, z) is the Bergman kernel for Ω.

• Journal of the Korean Mathematical Society
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• v.37 no.2
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• pp.253-267
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• 2000

• East Asian mathematical journal
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• v.9 no.1
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• pp.187-199
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• 1993

• Honam Mathematical Journal
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• v.37 no.3
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• pp.335-337
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• 2015

We modify the normalizing constants of the functions in the orthonormal basis for the Bergman space and restate their consequences in the paper that was published in Honam Math. J. 36 (2014), no. 4, pp. 777-786.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.375-383
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• 2009

In this note, we determine the properties of the coefficients of Bell domains in the plane and find some coefficients to consist of Bell domain.