• Title, Summary, Keyword: Bloch-type 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 ${\omega}$.

GENERALIZED COMPOSITION OPERATORS FROM GENERALIZED WEIGHTED BERGMAN SPACES TO BLOCH TYPE SPACES

  • Zhu, Xiangling
    • 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.

COMPACT INTERTWINING RELATIONS FOR COMPOSITION OPERATORS BETWEEN THE WEIGHTED BERGMAN SPACES AND THE WEIGHTED BLOCH SPACES

  • Tong, Ce-Zhong;Zhou, Ze-Hua
    • Journal of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.125-135
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    • 2014
  • We study the compact intertwining relations for composition operators, whose intertwining operators are Volterra type operators from the weighted Bergman spaces to the weighted Bloch spaces in the unit disk. As consequences, we find a new connection between the weighted Bergman spaces and little weighted Bloch spaces through this relations.

LIPSCHITZ TYPE INEQUALITY IN WEIGHTED BLOCH SPACE Bq

  • Park, Ki-Seong
    • Journal of the Korean Mathematical Society
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    • v.39 no.2
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    • pp.277-287
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    • 2002
  • Let B be the open unit ball with center 0 in the complex space $C^n$. For each q>0, B$_{q}$ consists of holomorphic functions f : B longrightarrow C which satisfy sup z $\in$ B $(1-\parallel z \parallel^2)^q\parallel\nabla f(z)\parallel < \infty$ In this paper, we will show that functions in weighted Bloch spaces $B_{q}$ (0 < q < 1) satifies the following Lipschitz type result for Bergman metric $\beta$: |f(z)-f($\omega$)|< $C\beta$(z, $\omega$) for some constant C.

INTEGRAL REPRESENTATION OF SOME BLOCH TYPE FUNCTIONS IN ℂn

  • Choi, Ki Seong;Yang, Gye Tak
    • Journal of the Chungcheong Mathematical Society
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    • v.10 no.1
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    • pp.17-22
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    • 1997
  • Let B be the open unit ball in the complex space $\mathbb{C}^n$. A holomorphic function $f:B{\rightarrow}C$ which satisfies sup{(1- ${\parallel}\;{\nabla}_zf\;{\parallel}\;{\mid}z{\in}B$} < $+{\infty}$ is called Bloch type function. In this paper, we will find some integral representation of Bloch type functions.

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Generalized Integration Operator between the Bloch-type Space and Weighted Dirichlet-type Spaces

  • Ardebili, Fariba Alighadr;Vaezi, Hamid;Hassanlou, Mostafa
    • Kyungpook Mathematical Journal
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    • v.60 no.3
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    • pp.519-534
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    • 2020
  • Let H(𝔻) be the space of all holomorphic functions on the open unit disc 𝔻 in the complex plane ℂ. In this paper, we investigate the boundedness and compactness of the generalized integration operator $$I^{(n)}_{g,{\varphi}}(f)(z)=\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^z\;f^{(n)}({\varphi}({\xi}))g({\xi})\;d{\xi},\;z{\in}{\mathbb{D}},$$ between Bloch-type and weighted Dirichlet-type spaces, where 𝜑 is a holomorphic self-map of 𝔻, n ∈ ℕ and g ∈ H(𝔻).