• Communications of the Korean Mathematical Society
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• v.12 no.1
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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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• v.5 no.2
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• pp.127-134
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• 1997

On the setting of the upper half-space of the euclidean n-space, we study some properties of harmonic little Bloch functions and we show that for a given harmonic little Bloch function $u$, there exists unique harmonic conjugates of $u$, which are also little Bloch functions with appropriate norm bounds.

• Korean Journal of Mathematics
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• v.11 no.2
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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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• v.7 no.2
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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.

• East Asian mathematical journal
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• v.28 no.1
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• pp.73-79
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• 2012

It is well-known that the BMO norm is equivalent to the Garsia norm. In this paper, we characterize mean-Lipschitz spaces by using Garsia-type norms on the upper half space $\mathbb{R}_+^{n+1}$.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.975-1002
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• 2005

On the setting of the upper half-space H of the Eu­clidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < $\infty$ and nonorthogonal projections for 1 $\leq$ p < $\infty$ . Using these results, we show that Bergman norm is equiva­ lent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we find the dual of b$\_{$^{1}$.

• 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.

• Journal of the Korean Mathematical Society
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• v.62 no.4
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• pp.811-834
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• 2025

In this paper, we establish the half-plane analogue of P. Ahern and Ž. Čučković [2] characterization of almost subharmonicity of functions satisfying the inequality 𝓑f ≥ f, where 𝓑 denotes the Berezin transform. As a byproduct, we investigate hyponormality of a class of Toeplitz operators with bounded harmonic symbols acting on the Bergman space of the complex upper half-plane.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1277-1288
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• 2013

Wulan and Zhu [16] have characterized the weighted Bergman space in the setting of the unit ball of $C^n$ in terms of Lipschitz type conditions in three different metrics. In this paper, we study characterizations of the harmonic Bergman space on the upper half-space in $R^n$. Furthermore, we extend harmonic analogues in the setting of the unit ball to the full range 0 < p < ${\infty}$. In addition, we provide the application of characterizations to showing the boundedness of a mapping defined by a difference quotient of harmonic function.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1337-1346
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• 2017

We define Bloch-type spaces of ${\mathcal{C}}^1({\mathbb{H}})$ on the upper half plane H and characterize them in terms of weighted Lipschitz functions. We also discuss the boundedness of a composition operator ${\mathcal{C}}_{\phi}$ acting between two Bloch spaces. These obtained results generalize the corresponding known ones to the setting of upper half plane.