单位球上小Bloch型空间之间的加权复合算子

数学物理学报 ›› 2010, Vol. 30 ›› Issue (4): 894-907.

单位球上小Bloch型空间之间的加权复合算子

刘竟成, 张学军

湖南师范大学数学与计算机科学学院, 长沙 410081

收稿日期:2008-09-30 修回日期:2009-10-13 出版日期:2010-07-25 发布日期:2010-07-25
基金资助:
国家自然科学基金(10871065)、湖南省自然科学基金(06JJ50010)和湖南省研究生创新基金(CX2009B099)资助

The Weighted Composition Operators between Little Bloch Type Spaces on the Unit Ball of CⁿStrong Approximations of Linear Processes

LIU Jing-Cheng, ZHANG Xue-Jun

College of |Mathematics and Computer Science, Hunan Normal University, Changsha 4100081

Received:2008-09-30 Revised:2009-10-13 Online:2010-07-25 Published:2010-07-25
Supported by:
国家自然科学基金(10871065)、湖南省自然科学基金(06JJ50010)和湖南省研究生创新基金(CX2009B099)资助

摘要/Abstract

摘要：

对所有的0<p、q<∞, 该文得到了Cⁿ中单位球上小Bloch型空间β^p₀到β^q₀之间的加权复合算子T_ψ,φ为有界算子或紧算子的充要条件.

关键词: 小Bloch型空间, 有界性, 紧性, 加权复合算子

Abstract:

In this paper, the necessary and sufficient conditions are given for the weighted composition operator T_ψ, _φ to be bounded or compact from little Bloch type spaces β^p₀ to β^q₀ for all 0<p<∞ and 0<q<∞ on the unit ball of Cⁿ.

Key words: Little Bloch type space, Boundedness, Compactness, Weighted composition operator

中图分类号:

47B38

刘竟成, 张学军. 单位球上小Bloch型空间之间的加权复合算子[J]. 数学物理学报, 2010, 30(4): 894-907.

LIU Jing-Cheng, ZHANG Xue-Jun. The Weighted Composition Operators between Little Bloch Type Spaces on the Unit Ball of CⁿStrong Approximations of Linear Processes[J]. Acta mathematica scientia,Series A, 2010, 30(4): 894-907.

参考文献

[1] Yang W S, Ouyang C H. Exact location of α-Bloch spaces in L^p_α and H^p of a complex unit ball. Rocky Mountain J math, 2000, 30: 1151--1169

[2] Zhou W X, Yang Y S. Integral criteria of Bloch functions on radial derivative. Acta Math Sci, 1998, 18: 451--458

[3] Madigan K, Matheson A. Compact composition operators on the Bloch space. Trans Amer Math Soc, 1995, 347: 2679--2687

[4] Zhao R H. Composition operators from Bloch type spaces to Hardy and Besov spaces. J Math Anal Appl, 1999, 233: 749--766

[5] Xiao J. Composition operators associated with Bloch type spaces. Complex Variables Theory Appl, 2001, 46: 109--121

[6] 张学军. p-Bloch空间上的复合算子和加权复合算子. 数学年刊, 2003, 24A(6): 711--720

[7] Madigan K. Composition operators on analytic Lipschitz spaces. Proc Amer Math Soc, 1993, 119: 465--473

[8] Ohno S, Zhao R H. Weighted composition operators on the Bloch space. Bull Austral Math Soc, 2001, 63: 177--185

[9] Ren G B, Shi J H. Bergman type operators on mixed spaces with application. Chin Ann of Math, 1997, 18B(3): 265--276

[10] Shi J H, Luo L. Composition operators on the Bloch space of several complex variables. Acta Math Sinica (English Series), 2000, 16: 85--98

[11] Zhou Z H, Zeng H G. Composition operators between p-Bloch space and $q$-Bloch space in the unit ball. Progress in Natural Science, 2003, 13: 233--236

[12] 刘竟成, 李菊香, 张学军. 超球上Bloch型空间之间复合算子再刻画. 数学学报, 2007, 50(3): 711--720

[13] 张学军, 刘竟成. 加权Bergman空间到$\mu$-Bloch空间的复合算子. 数学年刊, 2007, 28A(2): 255--266

[14] 叶善力, 高进寿. 有界对称域上的VMO$^p$与VO空间的乘子.数学物理学报, 2006, 26(1): 69--78

[15] 张学军. Cⁿ中Dirichlet型空间和Bloch型空间上的加权Cesàro算子. 数学年刊, 2005, 26A(1): 139--150

[16] Zhu K H. Spaces of Holomorphic Functions in the Unit Ball. New York: Springer-Verlag (GTM 226), 2004

[17] Zhuo W X, Ouyang C H. Möbius invariant gradient and little α-Bloch function. Acta Math Sci, 2002, 22B(3): 295--301

[18] 卓文新. 球上的Bloch函数的导数与$\alpha$-Carleson测度. 数学物理学报, 1994, 14(3): 351--360

[19] 王茂发, 刘云. 不同Bers型空间之间的加权复合算子. 数学物理学报, 2007, 27(4): 665--671