• 대한수학회논문집
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• 제12권1호
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• pp.51-58
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• 1997

On the setting of the upper half-space, H of the euclidean n-space, we consider the question of when the Poisson integral of a function on the boundary of H is a harmonic Bergman function and here we give a partial answer.

• Korean Journal of Mathematics
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• 제11권2호
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• pp.85-91
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• 2003

On the setting of the upper half-space of the euclidean space $\mathbf{R}^n$, we show some properties of weighted harmonic Bergman functions.

• Korean Journal of Mathematics
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• 제7권2호
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• pp.271-280
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• 1999

We study Toeplitz operators on the harmonic Bergman Space $b^p(\mathbf{H})$, where $\mathbf{H}$ is the upper half space in $\mathbf{R}(n{\geq}2)$, for 1 < $p$ < ${\infty}$. We give characterizations for the Toeplitz operators with positive symbols to be bounded.

• 대한수학회논문집
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• 제18권3호
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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.

• 대한수학회논문집
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• 제26권2호
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• pp.215-227
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• 2011

In this paper we introduce a class $h^{-\infty}_{\Phi}(\mathbb{B})$ of weighted spaces of harmonic functions in the unit ball $\mathbb{B}$ of $\mathbb{R}^n$. We dene weakly sufficient sets in this space and give an explicit construction of countable sets of such a type. Various examples of weight functions are also discussed.

• 대한수학회보
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• 제59권5호
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• pp.1167-1176
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• 2022

In this paper, we study Einstein-type manifolds generalizing static spaces and V-static spaces. We prove that if an Einstein-type manifold has non-positive complete divergence of its Weyl tensor and non-negative complete divergence of Bach tensor, then M has harmonic Weyl curvature. Also similar results on an Einstein-type manifold with complete divergence of Riemann tensor are proved.

• 대한수학회보
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• 제52권3호
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• pp.699-705
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• 2015

Two well known facts from elementary number theory are proven by using Bergman spaces.

• 대한수학회논문집
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• 제38권1호
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• pp.195-203
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• 2023

Special examples of harmonic manifolds that are not symmetric, proving that the conjecture posed by Lichnerowicz fails in the non-compact case have been intensively studied. We completely classify homogeneous structures on Damek-Ricci spaces equipped with the left invariant metric.

• Kyungpook Mathematical Journal
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• 제11권1호
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• pp.1-8
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• 1971

• 대한수학회보
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• 제46권2호
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• pp.263-279
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• 2009

On the setting of the unit ball of ${\mathbb{R}}^n$, we consider a Banach space of harmonic functions motivated by the atomic decomposition in the sense of Coifman and Rochberg [5]. First we identify its dual (resp. predual) space with certain harmonic function space of (resp. vanishing) logarithmic growth. Then we describe these spaces in terms of boundedness and compactness of certain Toeplitz operators.