| Zygmund空间上的微分复合算子 |
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| 引用本文： | 叶善力,林彩淑.Zygmund空间上的微分复合算子[J].数学学报,2016,59(1):11-20. |
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| 作者姓名： | 叶善力 林彩淑 |
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| 作者单位： | 1.浙江科技学院理学院 杭州 310023;2.福建师范大学数学与计算机科学学院 福州 350007 |
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| 基金项目： | 福建省自然科学基金资助项目(2015J01005)及省属高校专项基金资助项目(JK2012010) |
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| 摘 要： | 讨论Zygmund空间E={f∈H(D):sup_(z∈D)(l-|z|~2)|f″(z)|∞}上的微分复合算子DC_φ,这里C_φ是复合算子,D是微分算子.得到了DC_φ在Zygmund空间E和小Zygmund空间E_0上是有界算子与紧算子的充分必要条件.
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| 关 键 词： | Zygmund空间 微分算子 复合算子 |
Composition Followed by Differentiation on the Zygmund Space |
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| Shan Li YE,Cai Shu LIN.Composition Followed by Differentiation on the Zygmund Space[J].Acta Mathematica Sinica,2016,59(1):11-20. |
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| Authors: | Shan Li YE Cai Shu LIN |
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| Institution: | 1.School of Sciences, Zhejiang University of Science and Technology, Hangzhou 310023, P. R. China;2.School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, P. R. China |
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| Abstract: | We consider linear product operator DCφ acting on the Zygmund space Z = {f ∈H(D) : supz∈D(1-|z|2)|f" (z)|< ∞}, where Cφ is the composition operator and D is the differentiation operator. The boundedness and compactness of the operator DCφ on the Zygmund space Z and the little Zygmund space Z0 are established in terms of the function theorectic property of the symbol φ. |
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| Keywords: | Zygmund space differentiation operator composition operator |
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