• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1159-1170
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• 2020

We consider the weighted spaces ℓ^p(𝕊, 𝜑) and ℓ^p(𝕊, 𝜓) for 1 < p < +∞, where 𝜑 and 𝜓 are weights on 𝕊 (= ℕ or ℤ). We obtain a sufficient condition for ℓ^p(𝕊, 𝜓) to be multiplier weighted-space of ℓ^p(𝕊, 𝜑) and ℓ^p(𝕊, 𝜓). Our condition characterizes the last multiplier weighted-space in the case where 𝕊 = ℤ. As a consequence, in the particular case where 𝜓 = 𝜑, the weighted space ℓ^p(ℤ,𝜓) is a convolutive algebra.

• 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.52 no.5
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• pp.1711-1719
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• 2015

We obtain a new criterion for the boundedness and compactness of the weighted composition operators ${\psi}C_{\varphi}$ from ${\ss}^{{\alpha}}$(0 < ${\alpha}$ < 1) to ${\ss}^{{\beta}}$ in terms of the sequence $\{{\psi}{\varphi}^n\}$. An estimate for the essential norm of ${\psi}C_{\varphi}$ is also given.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1561-1576
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• 2008

In this paper we shall prove some weighted norm inequalities of the form $${\int}_{R^n}\;|Tf(x)|^pu(x)dx\;{\leq}\;C_p\;{\int}_{R^n}\;|f(x)|^pNu(x)dx$$ for certain rough singular integral T and maximal singular integral $T^*$. Here u is a nonnegative measurable function on $R^n$ and N denotes some maximal operator. As a consequence, some vector valued inequalities for both T and $T^*$ are obtained. We shall also get a boundedness result of T on the Triebel-Lizorkin spaces.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.507-514
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• 2018

Let $\{{\varphi}_n\}_{n{\geq}1}$ be a sequence of analytic self-maps of ${\mathbb{D}}$. It is proved that if the union set of the ranges of the composition operators $C_{{\varphi}_n}$ on the weighted Bergman spaces contains the disk algebra, then ${\varphi}_k$ is an automorphism of ${\mathbb{D}}$ for some $k{\geq}1$.

• 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.

• Communications of the Korean Mathematical Society
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• v.2 no.1
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• pp.33-37
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• 1987

• Bulletin of the Korean Mathematical Society
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• v.18 no.1
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• pp.17-19
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• 1981

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1195-1204
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• 2014

We newly define the volume integral means of harmonic functions to characterize the weighted harmonic Bergman spaces. It is based on Xiao and Zhu's results on holomorphic Bergman spaces [5].

• 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.