• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1171-1180
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• 2010

In this paper we obtain some new characterizations for weighted Bergman spaces in the unit ball of $\mathbb{C}^n$.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.307-317
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• 2004

In the setting of the half-plane of the complex plane, we show that for $r\geq0$, the dual space of the weighted bergman spaces B$^{1}{\gamma}$ is the Bloch space of the half-plane and we study some bounded linear operators induced by radial derivatives.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.147-164
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• 2008

In the setting of the half-plane of the complex plane, we show that for r > $-{\frac{1}{2}}$, the dual space of the weighted Bergman spaces $B^{1,r}$ is the Bloch space and we introduce some operators. We also study Toeplitz and Hankel operators and we find some characterization of Hankel operators.

• 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.60 no.5
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• pp.1201-1219
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• 2023

We characterize the boundedness and compactness of differences of weighted composition operators acting from weighted Bergman spaces A^p_ω to Lebesgue spaces L^q(dµ) for all 0 < p, q < ∞, where ω is a radial weight on the unit disk admitting a two-sided doubling condition.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1219-1232
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• 2009

Let H(B) denote the space of all holomorphic functions on the unit ball B of $\mathbb{C}^n$. Let $\varphi$ = (${\varphi}_1,{\ldots}{\varphi}_n$) be a holomorphic self-map of B and $g{\in}2$(B) with g(0) = 0. In this paper we study the boundedness and compactness of the generalized composition operator $C_{\varphi}^gf(z)=\int_{0}^{1}{\mathfrak{R}}f(\varphi(tz))g(tz){\frac{dt}{t}}$ from generalized weighted Bergman spaces into Bloch type spaces.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.618-627
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• 2022

On the setting of the orthogonal complement of the weighted Bergman space, we study the problem of when a finite sum of dual Toeplitz products is compact or zero. Our results extend several known results on the unweighted space to the weighted spaces.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.767-779
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• 2021

Schatten-Herz class Toeplitz operators on weighted Bergman spaces induced by doubling weights are investigated in this paper.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.311-317
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• 2013

In this note we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Weighted Bergman space $A^2_{\alpha}(\mathbb{D})$ with symbol in the class of functions $f+\bar{g}$ with polynomials $f$ and $g$ of degree 2.

• 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 $B^{1,r}$.