广西师范大学学报（自然科学版） ›› 2015, Vol. 33 ›› Issue (2): 64-67.doi: 10.16088/j.issn.1001-6600.2015.02.010

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一类广义Cesàro算子的紧致性研究

张太忠1, 陆恒1, 成亚萍2, 3   

  1. 1.南京信息工程大学数学与统计学院,江苏南京210044;
    2.南京信息工程大学江苏省网络监控中心,江苏南京210044;
    3.南京信息工程大学计算机与软件学院,江苏南京210044)
  • 收稿日期:2015-03-23 出版日期:2015-02-10 发布日期:2018-09-20
  • 通讯作者: 张太忠(1967—),男,江苏金湖人,南京信息工程大学教授。 E-mail: zhangspaces@163.com
  • 基金资助:
    国家自然科学基金资助项目(41174165);江苏省高校自然科学基础研究项目(07KJB110069)

A Study on a Kind of Compact Extended Cesàro Operators

ZHANG Tai-zhong1, LU Heng1, CHENG Ya-ping2, 3   

  1. 1.School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing Jiangsu210044, China;
    2.Jiangsu Engineering Center of Network Monitoring, Nanjing University of Information Scienceand Technology, Nanjing Jiangsu 210044, China;
    3.School of Computer and Software, Nanjing Universityof Information Science and Technology, Nanjing Jiangsu 210044, China
  • Received:2015-03-23 Online:2015-02-10 Published:2018-09-20

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摘要： 许多学者研究过由复平面单位圆上全纯函数构成的QK空间和Bloch空间,其中K(r)为(0,+∞)上右连续非负非减函数。这2个空间之间的Cesàro算子的紧致性的刻画是一个十分困难的问题。设0<α<+∞,且∫10(1-r2)-1K(-logr)rdr<+∞,g为单位圆上全纯函数,本文得到了从单位圆上QK空间到 α-Bloch空间的广义Cesàro算子Tg紧致的一个充分且必要条件。

关键词: QK空间, Bloch空间, Cesàro算子

Abstract: Many scholars studied the QK spaces and the Bloch space of holomorphic functions in the unit disk in the complex plane, where K(r) are right continuous nondecreasing functions on (0,+∞). However, it is very difficult to describe the compact Cesàro operators between these spaces. Let 0<α<+∞ and ∫10(1-r2)-1K(-logr)rdr<+∞,g is a holomorphic function in the unit disk, thus, a sufficient and necessary condition for the extended Cesàro operators Tg from QK spaces into α-Bloch spaces in the unit disc to be compact is obtained.

Key words: QK spaces, Bloch type spaces, extended Cesàro operator

中图分类号: 

  • O174.56
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