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Weighted Composition Operators from the Minimal M枚bius Invariant Space into the Bloch Space
- 作者:Flavia Colonna (1)
Songxiao Li (2)
- 关键词:Primary 47B33 ; Secondary 30H30 ; Weighted composition operator ; minimal m枚bius invariant space ; Bloch space
- 刊名:Mediterranean Journal of Mathematics
- 出版年:2013
- 出版时间:February 2013
- 年:2013
- 卷:10
- 期:1
- 页码:395-409
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Appl. 2007, Article ID 28629. 23. S. Stevi膰, / Essential norms of weighted composition operators from the 伪鈭?em class="a-plus-plus">Bloch / space to a weighted-type space on the unit ball, Abstr. Appl. Anal. 2008, Article ID 279691. 24. Stevi膰 S.: Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball. Appl. Math. Comput. 212, 499鈥?04 (2009) CrossRef 25. Stevi膰 S.: On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball. J. Math. Anal. Appl. 354, 426鈥?34 (2009) CrossRef 26. Stevi膰 S.: On a new integral operator between Bloch-type spaces on the unit ball. Bull. Sci. Math. 134, 329鈥?39 (2010) CrossRef 27. M. Tjani, / Compact composition operators on some M枚bius invariant Banach space, Ph.D. thesis, Michigan State University, 1996. 28. Tjani M.: Compact composition operators on Besov spaces. Trans. Amer. Math. Soc. 355, 4683鈥?698 (2003) CrossRef 29. H. Wulan and C. 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- 作者单位:Flavia Colonna (1)
Songxiao Li (2)
1. Department of Mathematical Sciences, George Mason University, Fairfax, VA, 22030, U.S.A. 2. Department of Mathematics, JiaYing University, 514015, Meizhou, GuangDong, China
- ISSN:1660-5454
文摘
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 M枚bius invariant space into the Bloch space and the little Bloch space.
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