• Title, Summary, Keyword: Bloch space

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BLOCH-TYPE SPACE RELATED WITH NORMAL FUNCTION

  • Choi, Ki Seong
    • 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 ${\omega}$.

A WEIGHTED COMPOSITION OPERATOR ON THE LOGARITHMIC BLOCH SPACE

  • Ye, Shanli
    • 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 ${\mathcal{L}\ss_0$.

HARMONIC LITTLE BLOCH FUNCTIONS ON THE UPPER HALF-SPACE

  • Yi, HeungSu
    • 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.

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WEIGHTED BLOCH SPACES IN $C^n$

  • Kyong Taik Hahn;Ki Seong Choi
    • 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 $q \geq 1$.

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WEIGHTED COMPOSITION OPERATORS FROM BERGMAN SPACES INTO WEIGHTED BLOCH SPACES

  • LI SONGXIAO
    • 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.

OPERATORS ON GENERALIZED BLOCH SPACE

  • Choi, Ki-Seong;Yang, Gye-Tak
    • The Pure and Applied Mathematics
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    • v.5 no.1
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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 $B_{q}$.

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