An integral-type operator from the minimal Mobius invariant space into the Bloch type space
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摘要: 利用分析和构造检验函数给出了积分型算子$C_\varphi ^g $从最小的M$\ddot{\rm o}$bius不变空间到 Bloch\,型空间的有界性和紧性的一些新的等价条件. 这些等价条件更加完整地刻画了$C_\varphi^g $, 也为其他积分型算子的研究提供很好的参考价值.
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关键词:
- Mobius不变空间 /
- Bloch型空间 /
- 积分型算子
Abstract: By using analysis methods and constructing test functions we obtained some new equivalent conditions for the boundedness and compactness of the integral-type operator $C_\varphi ^g $ from the minimal M$\ddot{\rm o}$bius invariant space into the Bloch-type space. These equivalent conditions give perfect characterizations of $C_\varphi ^g $, which also provide good reference for the study of other integral-type operators.-
Key words:
- Mobius invariant space /
- Bloch-type space /
- integral-type operator
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{[1]} ZHU K H. Spaces of Holomorphic Functions in the Unit Ball[M]. New York: Springer, 2004. {[2]} COLONNA F, LI S X. Weighted composition operators from the minimal Mobius invariant space into the Bloch space[J]. Mediterr J Math, DOI 10. 1007/s00009-012-0182-8.{[3]} LI S X. weighted composition operators from Minimal Mobius invariant spaces to Zygmund spaces[J]. Filomat, 2013(2): 269-277.{[4]} YAMASHITA S. Gap series and $\alpha $-Bloch functions[J]. Yokohama Math J, 1980, 28: 31-36.{[5]} LI S X, STEVIC' S. Generalized composition operators on Zygmund spaces and Bloch type spaces[J]. Math Anal Appl, 2008, 338: 1282-1295.{[6]} LI S X, STEVIC` S. Products of integral-type operators and composition operators between Bloch-type spaces[J]. Math Anal Appl, 2009, 349: 596-610.{[7]} COWEN C C, MACCLUER B D. Composition Operators on Spaces of Analytic Functions[M]. Boca Raton, FL: CRC Press, 1995.
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