Bloch型空间到对数Bloch型空间的加权复合算子紧性特征
|
摘要
基于复分析和算子理论技巧,运用泛函分析与调和分析的方法刻画了Bloch型空间到对数Bloch空间和小对数Bloch空间的加权复合算子T_(u,φ)的有界性与紧性特征,并获得了该加权复合算子T_(u,φ)为有界与紧的充要条件,通过不同的α取值范围得到不同的充要条件,其中u为单位圆盘上的解析函数,φ为D上的解析自映射。
Based on complex analysis and operator theory, we characterizes the bounded and compactness of the weight composition T_(uφ) from Bloch type space to Logarith Bloch type space and little Logarith Bloch type space. Different necessary and sufficient conditions are obtained by different values of α, where u is an analytic function on the unit disk and φ is an analytic self-maple on the unit disk.
Based on complex analysis and operator theory, we characterizes the bounded and compactness of the weight composition T_(uφ) from Bloch type space to Logarith Bloch type space and little Logarith Bloch type space. Different necessary and sufficient conditions are obtained by different values of α, where u is an analytic function on the unit disk and φ is an analytic self-maple on the unit disk.
引文
[1] ZHU K H. Bloch type spaces of analytic functions[J]. The Rocky Mountain Journal of Mathematics, 1993, 23(3):1143-1177.
[2]韩金桩,吴玉田.对数Bloch型空间的高阶导数特征[J].安徽理工大学学报(自然科学版), 2014, 2(34):32-34.
[3]张学军,肖建斌.两个解析函数空间之间的加权复合算子[J].数学进展, 2006, 35(4):453-462.
[4]张学军. p-Bloch空间上的复合算子与加权复合算子[J].数学年刊, 2003, 24A(6):711-720.
[5]朱克超,吴鹏程. Bα空间到QK空间的加权复合算子[J].贵州师范大学学报(自然科学版), 2010, 28(1):95-99.
[6] LI S X, ZHOU J Z. A note of weighted composition operators on Blohc type spaces[J]. Bulletin of the Korean Mathematical Society, 2015,52(5):1711-1719.
[7] OHNO S C, ZHAO R H. Weighted composition operators on the Bloch space[J]. Bulletin of the Australian Mathematical Society, 2001, 63:177-185.
[8]张学军. Cn中Dirchlet型空间和Bloch型空间上的加权Cesarari算子[J].数学年刊A辑(中文版),2005, 26(1):139-150.
[9] YE S L. Weighted composition operators from F(p,q,s)into logarithmic Bloch space[J]. Bulletin of the Korean Mathematical Society,2008, 45(4):977-991.
[10] LOU Z J. Composition operators on Bloch type spaces[J]. Analysis, 2003, 23(1):81-95.
[2]韩金桩,吴玉田.对数Bloch型空间的高阶导数特征[J].安徽理工大学学报(自然科学版), 2014, 2(34):32-34.
[3]张学军,肖建斌.两个解析函数空间之间的加权复合算子[J].数学进展, 2006, 35(4):453-462.
[4]张学军. p-Bloch空间上的复合算子与加权复合算子[J].数学年刊, 2003, 24A(6):711-720.
[5]朱克超,吴鹏程. Bα空间到QK空间的加权复合算子[J].贵州师范大学学报(自然科学版), 2010, 28(1):95-99.
[6] LI S X, ZHOU J Z. A note of weighted composition operators on Blohc type spaces[J]. Bulletin of the Korean Mathematical Society, 2015,52(5):1711-1719.
[7] OHNO S C, ZHAO R H. Weighted composition operators on the Bloch space[J]. Bulletin of the Australian Mathematical Society, 2001, 63:177-185.
[8]张学军. Cn中Dirchlet型空间和Bloch型空间上的加权Cesarari算子[J].数学年刊A辑(中文版),2005, 26(1):139-150.
[9] YE S L. Weighted composition operators from F(p,q,s)into logarithmic Bloch space[J]. Bulletin of the Korean Mathematical Society,2008, 45(4):977-991.
[10] LOU Z J. Composition operators on Bloch type spaces[J]. Analysis, 2003, 23(1):81-95.