• 호남수학학술지
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• 제30권1호
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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.

• 대한수학회지
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• 제36권5호
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• pp.855-890
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• 1999

Necessary and sufficient conditions on the weight functions u(.) and $\upsilon$(.) are derived in order that the fractional maximal operator $M\alpha,\;0\;\leq\;\alpha\;<\;1$, is bounded from the weighted amalgam space $\ell^s(L^p(\mathbb{R},\upsilon(x)dx)$ into $\ell^r(L^q(\mathbb{R},u(x)dx)$ whenever $1\leq s\leq r<\infty\;and\;1. The boundedness problem for the fractional intergral operator $I_{\alpha},0<\alpha\leq1$, is also studied.

• 대한수학회보
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• 제44권4호
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• pp.701-708
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• 2007

In this paper we characterize the boundedness, compactness and closedness of the range of the weighted composition operators on Lorentz spaces L(p,q), $1.

• 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.

• 대한수학회논문집
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• 제21권4호
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• pp.719-727
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• 2006

In this paper, we study the boundedness and the com-pactness of weighted composition operator between $H^{\infty}$ and Bergman type space on the unit ball of $\mathbb{C}^n$. Also, the norm of corresponding weighted composition operator is computed.

• 충청수학회지
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• 제13권1호
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• pp.131-138
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• 2000

Let D be the open unit disk in the complex plane $\mathbb{C}$. For any q > 0, the operator $Q_q$ defined by $$Q_qf(z)=q\int_{D}\frac{f(\omega)}{(1-z{\bar{\omega}})^{1+q}}d{\omega},\;z{\in}D$$. maps $L^{\infty}(D)$ boundedly onto $B_q$ for each q > 0. In this paper, weighted Bloch spaces $\mathcal{B}_q$ (q > 0) are considered on the open unit ball in $\mathbb{C}^n$. In particular, we will investigate the possibility of extension of this operator to the Weighted Bloch spaces $\mathcal{B}_q$ in $\mathbb{C}^n$.

• 대한수학회보
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• 제57권3호
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• pp.583-595
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• 2020

Let HE_I, HE_II, HE_III and HE_IV be the first, second, third and fourth type Loo-Keng Hua domain respectively, 𝜑 a holomorphic self-map of HE_I, HE_II, HE_III, or HE_IV and u ∈ H(𝓜) the space of all holomorphic functions on 𝓜 ∈ {HE_I, HE_II, HE_III, HE_IV}. In this paper, motivated by the well known Hua's matrix inequality, first some inequalities for the points in the Bers-type spaces of the Loo-Keng Hua domains are obtained, and then the boundedness and compactness of the weighted composition operators W_𝜑,u : f ↦ u · f ◦ 𝜑 on Bers-type spaces of these domains are characterized.

• 충청수학회지
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• 제23권3호
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• pp.523-534
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• 2010

In this paper, we consider the weighted Bloch spaces ${\mathcal{B}}_q$(q > 0) on the open unit ball in ${\mathbb{C}}^n$. We prove a certain integral representation theorem that is used to determine the degree of growth of the functions in the space ${\mathcal{B}}_q$ for q > 0. This means that for each q > 0, the Banach dual of $L_a^1$ is ${\mathcal{B}}_q$ and the Banach dual of ${\mathcal{B}}_{q,0}$ is $L_a^1$ for each $q{\geq}1$.

• 호남수학학술지
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• 제37권4호
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• pp.387-395
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• 2015

We investigate conditions under which a holomorphic self-map of the unit disk induces a bounded composition operator and study some properties of the composition operator from the Bloch-type spaces into a generalization of the Bloch-type spaces.

• 대한수학회보
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• 제50권5호
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• pp.1451-1469
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• 2013

We present various new sharp assertions on multipliers in mixed norm, weighted Hardy and new Lizorkin-Triebel spaces of harmonic functions in higher dimension. Some results are new even in onedimensional case.