• 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.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.481-495
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• 2021

In this paper, we investigate the properties of Bergman spaces, Bloch spaces and integral means of p-harmonic functions on the unit ball in ℝn. Firstly, we offer some Lipschitz-type and double integral characterizations for Bergman space ��kγ. Secondly, we characterize Bloch space ��αω in terms of weighted Lipschitz conditions and BMO functions. Finally, a Hardy-Littlewood type theorem for integral means of p-harmonic functions is established.

• 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.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.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.773-786
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• 2001

On the setting of the half-space of the Euclidean n-space, we consider harmonic Bergman spaces and we also study properties of the reproducing kernel. Using covering lemma, we find some equivalent quantities. We prove that if lim$ lim\limits_{i\rightarrow\infty}\frac{\mu(K_r(zi))}{V(K_r(Z_i))}$ then the inclusion function $I : b^p\rightarrow L^p(H_n, d\mu)$ is a compact operator. Moreover, we show that if f is a nonnegative continuous function in $L^\infty and lim\limits_{Z\rightarrow\infty}f(z) = 0, then T_f$ is compact if and only if f $\in$ $C_{o}$ (H$_{n}$ ).

• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.419-428
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• 2006

The Berezin transform is the analogue of the Poisson transform in the Bergman spaces. Dyakonov characterize the holomorphic weighted Lipschitz function in the unit disk in terms of the Possion integral. In this paper, we characterize the harmonic weighted Lispchitz function in terms of the Berezin transform instead of the Poisson integral.