• 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.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.727-737
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• 2009

Let M(X) be the space of all pointwise multipliers of Banach space X. We will show that, for each $\alpha>1$, $M(\mathfrak{B}_\alpha)=M(\mathfrak{B}_{\alpha,0})=H^\infty{(B)}$. We will also show that, for each $0<{\alpha}<1$, $M(\mathfrak{B}_\alpha)$ and $M(\mathfrak{B}_{\alpha,0})$ are Banach algebras. It is established that certain inclusion relationships exist between the weighted Bloch spaces and holomorphic Besov spaces.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.159-165
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• 2010

A characterization of the holomorphic function spaces of mean Bloch type on the unit disc is deduced in terms of the induced distance.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1841-1851
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• 2017

Motivated by the Bloch-Beilinson conjectures, Voisin has made a conjecture concerning zero-cycles on self-products of Calabi-Yau varieties. We reformulate Voisin's conjecture in the setting of $hyperk{\ddot{a}}hler$ varieties, and we prove this reformulated conjecture for one family of $hyperk{\ddot{a}}hler$ fourfolds.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.57-66
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• 2009

In this paper, we characterize the boundedness and compactness of the extended $Ces{\grave{a}}ro$ operators from general function spaces F(p, q, s) to Bloch-type spaces ${\mathcal{B}}_{\mu}$ where $\mu$ is normal function on [0,1).

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1171-1180
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• 2018

In this paper, we prove that boundedness with respect to metric balls of weighted composition operators from the Kim class and the Smirnov class to weighted Bloch type spaces is equivalent to metrical compactness of weighted composition operators between these spaces.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.17-24
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• 1995

We begin with a brief survey of some of the known results dealing with Bloch constants. Bloch's theorem asserts that there is a constant B$\_$1.C/(1, 0) such that if f is holomorphic in the open unit disk D and normalized by │f'(0)│$\geq$1, then the Riemann surface of f contains an unramified disk of radius at least B$\_$1.C/(1, 0) (see[7,p.14]).(omitted)

• Journal of the Chungcheong Mathematical Society
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• v.14 no.2
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• pp.37-46
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• 2001

In this paper, weighted Bloch spaces $\mathcal{B}_q$ are considered on the open unit ball in $\mathbb{C}^n$. In this paper, we will show that every Bloch function in $B_q$ induces a bounded linear functional on $L^1_a(\mathcal{B})$.

• East Asian mathematical journal
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• v.37 no.1
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• pp.19-32
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• 2021

We estimate the Bergman metric of the exponentially weighted Bergman space and prove many different geometric characterizations for related Bloch spaces. In particular, we prove that the Bergman metric of the exponentially weighted Bergman space is comparable to some Poincaré type metric.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.467-474
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• 2022

In this article, we consider the integral operator 𝓒^b,c, which is defined as follows: $${\mathcal{C}}^{b,c}(f)(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\frac{f(w)*F(1,1;c;w)}{w(1-w)^{b+1-c}}}dw,$$ where * denotes the Hadamard/ convolution product of power series, F(a, b; c; z) is the classical hypergeometric function with b, c > 0, b + 1 > c and f(0) = 0. We investigate the boundedness of the 𝓒^b,c operators on Bloch spaces.