不同Bloch型空间之间的积型算子的紧性

房敏, 刘永民

数学学报 ›› 2017, Vol. 60 ›› Issue (4) : 661-668.

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数学学报 ›› 2017, Vol. 60 ›› Issue (4) : 661-668. DOI: 10.12386/A2017sxxb0055
论文

不同Bloch型空间之间的积型算子的紧性

    房敏1,2, 刘永民1
作者信息 +

The Compactness of Product-Type Operators Between Different Bloch Type Spaces

    Ming FANG1,2, Yong Min LIU1
Author information +
文章历史 +

摘要

利用Bloch型空间中函数的导数的估计,通过构造一些新的检验函数,运用解析函数的性质与算子理论,给出了不同Bloch型空间中的积型算子紧性的特征.

Abstract

In this paper,using the estimate of the derivative of the function in Bloch type spaces,the properties of the analytic function and operator theory,the authors characterize the compactness of product-type operators between different Bloch type spaces by means of constructing some test functions.

关键词

Bloch型空间 / 积型算子T&psi / 1 / &psi / 2 / &phi / / 紧性

Key words

Bloch type space / product-type operators Tψ1,ψ2,φ / compactness

引用本文

导出引用
房敏, 刘永民. 不同Bloch型空间之间的积型算子的紧性. 数学学报, 2017, 60(4): 661-668 https://doi.org/10.12386/A2017sxxb0055
Ming FANG, Yong Min LIU. The Compactness of Product-Type Operators Between Different Bloch Type Spaces. Acta Mathematica Sinica, Chinese Series, 2017, 60(4): 661-668 https://doi.org/10.12386/A2017sxxb0055

参考文献

[1] Bai H., Jiang Z., Generalized weighted composition operators from Zygmund spaces to Bloch-Orlicz type spaces, Appl. Math. Comput., 2016, 273:89-97.
[2] Fang M., Product type operators between different Bloch-type spaces (in Chinese), J. Jiangsu Norm. Univ. Nat. Sci. Ed., 2016, 34(2):25-28.
[3] Jiang Z., On Stevi?-Sharma operator from the Zygmund space to the Bloch-Orlicz space, Adv. Difference Equ., 2015, 2015:228, DOI 10.1186/s13662-015-0567-7.
[4] Jiang Z., On a product-type operator from weighted Bergman-Orlicz space to some weighted type spaces, Appl. Math. Comput., 2015, 256:37-51.
[5] Jiang Z., Generalized product-type operators from weighted Bergman-Orlicz spaces to Bloch-Orlicz spaces, Appl. Math. Comput., 2015, 268:966-977.
[6] Li H., Guo Z., On a product-type operator from Zygmund-type spaces to Bloch-Orlicz spaces, J. Inequal. Appl., 2015, 2015:132, DOI 10.1186/s13660-015-0658-8.
[7] Li S., Stevi? S., Generalized weighted composition operators from α-Bloch spaces into weighted-type spaces, J. Inequal. Appl., 2015, 2015:265, DOI 10.1186/s13660-015-0770-9.
[8] Liu X., Yu Y., The product of differentiation operator and multiplication operator from H∞ to Zygmund spaces, J. Xuzhou Norm. Univ. Nat. Sci. Ed., 2011, 29(1):37-39.
[9] Liu Y., Yu Y., On a Stevi?-Sharma operator from Hardy spaces to the logarithmic Bloch spaces, J. Inequal. Appl., 2015, 2015:22, DOI 10.1186/s13660-015-0547-1.
[10] Sharma A., Generalized composition operators between Hardy and weighted Bergman spaces, Acta Sci. Math. (Szeged), 2012, 78(1-2):187-211.
[11] Stevi? S., Sharma A., Bhat A., Products of multiplication composition and differentiation operators on weighted Bergman space, Appl. Math. Comput., 2011, 217:8115-8125.
[12] Wang Y., Shang Q., Boundedness and compactness of the Tu,φ△ from H∞ space to B(B0) space (in Chinese), J. Jiangsu Norm. Univ. Nat. Sci. Ed., 2016, 34(2):21-24.
[13] Wu Y., Wulan H., Products of differentiation and composition operators on the Bloch space, Collect. Math., 2012, 63(1):93-107.
[14] Ye S., A weighted composition operator between different weighted Bloch-type spaces (in Chinese), Acta Math. Sinica, Chin. Ser., 2007, 50(4):927-942.
[15] Ye S., Lin C., Composition followed by differentiation on the Zygmund space (in Chinese), Acta Math. Sinica, Chin. Ser., 2016, 59(1):11-20.
[16] Yu Y., Liu Y., Boundedness of product-type operators on the logarithmic Bloch spaces (in Chinese), Chinese Ann. Math. Ser. A, 2016, 37A(3):273-290.
[17] Zhang F., Liu Y., On the compactness of the Stevi?-Sharma operator on the logarithmic Bloch spaces, Math. Inequal. Appl., 2016, 19(2):625-642.
[18] Zhang X., Composition operators and weighted composition operators on p-Bloch spaces (in Chinese), Chinese Ann. Math. Ser. A, 2003, 24(6):711-720.
[19] Zhu K., Bloch type spaces of analytic functions, Rocky Mountain J. Math., 1993, 23(3):1143-1177.
[20] Zhu X., Essential norm and compactness of the product of differentiation and composition operators on Bloch type spaces, Math. Inequal. Appl., 2016, 19(1):325-334.

基金

国家自然科学基金资助项目(11171285);江苏高校品牌专业建设工程(PPZY2015A013);江苏省基础研究计划(BK20161158)和江苏省普通高校研究生科研创新计划(CXLX13-970)

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