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Weighted Composition Operators from the Minimal Möbius Invariant Space into the Bloch Space

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Abstract

Let \({{\varphi}}\) be an analytic self-map of the open unit disk \({{\mathbb{D}}}\) in the complex plane \({{\mathbb{C}, H(\mathbb{D})}}\) the space of complex-valued analytic functions on \({{\mathbb{D}}}\) , and let u be a fixed function in \({{H(\mathbb{D})}}\) . The weighted composition operator is defined by

$$(uC_{\varphi}f)(z) = u(z)f({\varphi}(z)), \quad z \in \mathbb{D}, f \in H(\mathbb{D}).$$

In this paper, we study the boundedness and the compactness of the weighted composition operators from the minimal Möbius invariant space into the Bloch space and the little Bloch space.

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Authors and Affiliations

  1. Department of Mathematical Sciences, George Mason University, Fairfax, VA, 22030, U.S.A.

    Flavia Colonna

  2. Department of Mathematics, JiaYing University, 514015, Meizhou, GuangDong, China

    Songxiao Li

Authors
  1. Flavia Colonna
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  2. Songxiao Li
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Correspondence to Flavia Colonna.

Additional information

The second author is supported by the Guangdong Natural Science Foundation (No. 10451401501004305) and by the National Natural Science Foundation of China (No. 11001107).

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Colonna, F., Li, S. Weighted Composition Operators from the Minimal Möbius Invariant Space into the Bloch Space. Mediterr. J. Math. 10, 395–409 (2013). https://doi.org/10.1007/s00009-012-0182-8

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  • DOI: https://doi.org/10.1007/s00009-012-0182-8

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