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GENERALIZED WEIGHTED COMPOSITION OPERATORS FROM AREA NEVANLINNA SPACES TO WEIGHTED-TYPE SPACES

  • Weifeng, Yang (Department of Mathematics and Physics Hunan Institute of Engineering) ;
  • Weiren, Yan (Department of Mathematics and Physics Hunan Institute of Engineering)
  • Received : 2010.06.30
  • Published : 2011.11.30
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Abstract

Let $H(\mathbb{D})$ denote the class of all analytic functions on the open unit disk $\mathbb{D}$ of the complex plane $\mathbb{C}$. Let n be a nonnegative integer, ${\varphi}$ be an analytic self-map of $\mathbb{D}$ and $u{\in}H(\mathbb{D})$. The generalized weighted composition operator is defined by $$D_{{\varphi},u}^nf=uf^{(n)}{\circ}{\varphi},\;f{\in}H(\mathbb{D})$$. The boundedness and compactness of the generalized weighted composition operator from area Nevanlinna spaces to weighted-type spaces and little weighted-type spaces are characterized in this paper.

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References

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