• 충청수학회지
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• 제24권3호
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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 ${\omega}$.

• 대한수학회보
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• 제47권3호
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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 ${\mathcal{L}\ss_0$.

• Korean Journal of Mathematics
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• 제5권2호
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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.

• 대한수학회논문집
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• 제20권1호
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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.

• 대한수학회지
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• 제35권1호
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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 $q \geq 1$.

• 대한수학회지
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• 제54권2호
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• pp.627-645
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• 2017

In this paper, we characterize the boundedness, compactness and essential norm of products of differentiation and composition operators from the Bloch space and weighted Dirichlet spaces to analytic Morrey type spaces.

• 대한수학회보
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• 제58권2호
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• pp.481-495
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• 2021

In this paper, we investigate the properties of Bergman spaces, Bloch spaces and integral means of p-harmonic functions on the unit ball in ℝn. Firstly, we offer some Lipschitz-type and double integral characterizations for Bergman space ��kγ. Secondly, we characterize Bloch space ��αω in terms of weighted Lipschitz conditions and BMO functions. Finally, a Hardy-Littlewood type theorem for integral means of p-harmonic functions is established.

• 대한수학회지
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• 제45권1호
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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.

• 대한수학회논문집
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• 제21권2호
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• pp.287-292
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• 2006

On the unit disk of the complex plane, a characterization of Bloch function is expressed extending known result.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권1호
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• pp.17-21
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• 1998

In [5], Zhu introduces a bounded operator T from $L^{\infty}$(D) into Bloch space B. In this paper, we will consider the generalized Bloch spaces $B_{q}$ and find bounded operator from $L^{\infty}$(D) into $B_{q}$.