• 제목/요약/키워드: Bloch space

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A WEIGHTED COMPOSITION OPERATOR ON THE LOGARITHMIC BLOCH SPACE

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

HARMONIC LITTLE BLOCH FUNCTIONS ON THE UPPER HALF-SPACE

  • Yi, HeungSu
    • 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.

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WEIGHTED COMPOSITION OPERATORS FROM BERGMAN SPACES INTO WEIGHTED BLOCH SPACES

  • LI SONGXIAO
    • 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.

WEIGHTED BLOCH SPACES IN $C^n$

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

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BERGMAN SPACES, BLOCH SPACES AND INTEGRAL MEANS OF p-HARMONIC FUNCTIONS

  • Fu, Xi;Qiao, Jinjing
    • 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.

OPERATORS ON GENERALIZED BLOCH SPACE

  • Choi, Ki-Seong;Yang, Gye-Tak
    • 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 $B_{q}$.

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