• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.533-541
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• 2011

Let ${\omega}$ be a normal function. In this paper, we will extend the concept of Bloch space to Bloch-type space related with normal function ${\omega}$. We will investigate the properties of Bloch-type space ${\mathcal{B}}_{\omega}$ and the little Bloch-type space ${\mathcal{B}}_{{\omega},0}$ with weight ${\omega}$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1591-1603
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• 2014

In this paper, we investigate maximum principle, convergence of sequences and angular limits for harmonic Bloch mappings. First, we give the maximum principle of harmonic Bloch mappings, which is a generalization of the classical maximum principle for harmonic mappings. Second, by using the maximum principle of harmonic Bloch mappings, we investigate the convergence of sequences for harmonic Bloch mappings. Finally, we discuss the angular limits of harmonic Bloch mappings. We show that the asymptotic values and angular limits are identical for harmonic Bloch mappings, and we further prove a result that applies also if there is no asymptotic value. A sufficient condition for a harmonic Bloch mapping has a finite angular limit is also given.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.127-134
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• 1997

On the setting of the upper half-space of the euclidean n-space, we study some properties of harmonic little Bloch functions and we show that for a given harmonic little Bloch function $u$, there exists unique harmonic conjugates of $u$, which are also little Bloch functions with appropriate norm bounds.

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.423-435
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• 2012

We give some properties of weak Bloch functions and also give some properties of ${\phi}$-uniform domains and ${\phi}$-John domains in terms of moduli of continuity of Bloch functions and weak Bloch functions.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.527-540
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• 2010

We characterize the boundedness and compactness of the weighted composition operator on the logarithmic Bloch space $\mathcal{L}\ss=\{f{\in}H(D):sup_D(1-|z|^2)ln(\frac{2}{1-|z|})|f'(z)|$<+$\infty$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$. The results generalize the known corresponding results on the composition operator and the pointwise multiplier on the logarithmic Bloch space ${\mathcal{L}\ss$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.439-454
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• 2014

We deal with the boundedness of the n-th derivatives of Bloch-type functions and Toeplitz operators and give a relationship between Bloch-type spaces and ranges of Toeplitz operators. Also we prove that the vanishing property of ${\parallel}uk^{\alpha}_z{\parallel}_{s,{\alpha}}$ on the boundary of $\mathbb{D}$ implies the compactness of Toeplitz operators and introduce a generalization of Bloch-type spaces.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.177-189
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• 1998

In this paper, weighted Bloch spaces $B_q (q > 0)$ are considered on the open unit ball in $C^n$. These spaces extend the notion of Bloch spaces to wider classes of holomorphic functions. It is proved that the functions in a weighted Bloch space admit certain integral representation. This representation formula is then used to determine the degree of growth of the functions in the space $B_q$. It is also proved that weighted Bloch space is a Banach space for each weight q > 0, and the little Bloch space $B_q,0$ associated with $B_q$ is a separable subspace of $B_q$ which is the closure of the polynomials for each $q \geq 1$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1135-1140
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• 2009

We will consider the questions of when the products of composition and differentiation are bounded and compact on Bloch and little Bloch spaces.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.63-70
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• 2005

In this paper we study bounded and compact weighted composition operator, induced by a fixed analytic function and an analytic self-map of the open unit disk, from Bergman space into weighted Bloch space. As a corollary, obtain the characterization of composition operator from Bergman space into weighted Bloch space.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.229-248
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• 2008

The boundedness and compactness of the Volterra composition operators between weighted Bergman spaces and Bloch type spaces are discussed in this paper.