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摘要:算子理论是解析函数空间理论研究的重要内容,为了寻找通过探讨联立算子与函数空间的方法研究算子以及函数空间的有效途径,假设 为单位圆盘Δ上的一个解析自映射,正规权Bloch空间μ-B是单位圆盘Δ上的一个Banach空间,定义C∶C(f)=f为μ-B上的复合算子,对所有的f∈μ-B,并由积分算子以及复合算子推广得到积分型算子JhC和CJh,主要讨论了正规权Bloch空间到QT,S空间的积分型算子JhC的有界性和紧性,以及正规权Bloch空间到QT,S空间的积分型算子CJh的有界性,并给出了相关的充要条件。
关键词:函数空间;正规权Bloch空间; QT,S空间; 积分型算子; 有界性; 紧性
中图分类号:O174.5; O177.2MSC(2010)主题分类:47B38文献标志码:A
文章编号:1008-1542(2016)04-0335-05
3结论
积分型算子由积分算子和复合算子推广得到,研究正规权Bloch空间到QT,S空间之间的积分型算子是有意义的。本文给出了正规权Bloch空间到QT,S空间的积分型算子JhC的有界性和紧性成立的充分必要条件,以及CJh的有界性成立的充分必要条件。
参考文献/References:
[1]COWEN C C, CLUER M. Composition Operators on Spaces of Analytic Functions[M]. Boca Roton:CRC Press,1995.
[2]LI Songxiao, STEVIC′ S. Products of integral-type operator and composition operators between Bloch-type spaces[J]. Journal of Mathematical Analysis & Applications, 2009,349(2):596-610.
[3]WU Pengcheng, WULAN H. Composition operators from the Bloch space into the spaces QT[J]. International Journal of Mathematics & Mathematical Sciences, 2003,2003(31): 1973-1979.
[4]LOU Zengjian. Composition operators on Bloch type space[J].Analysis, 2003,1(1): 81-95.
[5]WULAN H. Compactness of composition operators from the Bloch space B to QK spaces[J].Acta Mathematica Sinica, 2005,21(6): 1415-1424.
[6]刘光荣,宋修朝,梁国宏. α-Bloch到正规权Bloch空间的复合算子[J]. 汕头大学学报(自然科学版), 2010, 25(4):12-17.
LIU Guangrong,SONG Xiuchao,LIANG Guohong.Composition operator from α-Bloch spaces to normal Bloch spaces[J]. Journal of Shantou University(Natural Science Edition), 2010, 25(4): 12-17.
[7]YANG Congli,XU Wen,KOTILAINEN M.Composition operators from Bloch type spaces into QK spaces[J].Journal of Mathamatical Analysis and Appllisations,2011,379(1):26-34.
[8]YONEDA R. Integration operators on weighted Bloch spaces[J]. Nihonkai Mathematical Journal, 2001,12(2):123-133.
[9]STEVIC′ S. Boundedness and compactness of an integral operator on a weighted space on the polydisc[J]. Indian Journal of Pure & Applied Mathematics, 2006,37(6):343.
[10]STEVIC′ S. Boundedness and compactness of an integral operator between H∞ and a mixed norm space on the polydisk[J]. Sibirsk Mat Zh, 2007,48(3):559-569.
[11]STEVIC′ S. On a new operator from the logarithmic Bloch space to the Bloch-type space on the unit ball[J]. Applied Mathematics and Computation, 2008,206(1):313-320.
[12]YU Yanyan,LIU Yongmin. Integral-type operators from weighted Bloch spaces into Bergman-type spaces[J]. Integral Transforms & Special Functions,2009, 20(6):419-428. [13]李海英, 田长安,张相波. 单位球上的加权Bergman空间到加权Bloch空间的积分型算子[J]. 数学杂志, 2012, 32(6): 1100-1104.
LI Haiying,TIAN Changan,ZHANG Xiangbo.Integral-type operators from weighted Bergman spaces to weighted Bloch spaces on the unit ball[J]. Journal of Mathematics, 2012, 32(6): 1100-1104.
[14]SHIELDS A L, WILLIAMS D L. Bounded projections,duality,and multipliers in spaces of analytic functions[J]. Transactions of the American Mathematical Society,1971,162:287-302.
[15]STEVIC S. Norm of weighted composition operators from Bloch space to H∞μ on the unit ball[J]. Ars combinatoria,2008,88:125-127.
[16]FU Xiaohong, ZHU Xiangling. Weighted composition operators on some weighted spaces in the unit ball[J]. Abstract and Applied Analysis,2008,605(3):807-814.
[17]WULAN H. Mobius invariant QP space:results,techniques and questions[J]. Advances in Mathematics(China), 2005,34(4): 385-403.
[18]WULAN H, WU Pengcheng. Characterizations of QT spaces[J]. Journal of Mathematical Analysis Applicatons, 2001,254(2): 484-497.
[19]周江河, 谭海鸥. 关于解析QT,S空间[J]. 五邑大学学报(自然科学版), 2009, 23(3): 50-52.
ZHOU Jianghe,TAN Haiou.On analytic QT,S spaces[J]. Journal of Wuyi University(Natural Science Edition), 2009, 23(3): 50-52.
[20]YANG Congli,XU Wen,KOTILAINEN M. Composition operators from Bloch type spaces into QK spaces[J]. Journal of Mathematical Analysis Applicatons,2011,379(1):26-34.
关键词:函数空间;正规权Bloch空间; QT,S空间; 积分型算子; 有界性; 紧性
中图分类号:O174.5; O177.2MSC(2010)主题分类:47B38文献标志码:A
文章编号:1008-1542(2016)04-0335-05
3结论
积分型算子由积分算子和复合算子推广得到,研究正规权Bloch空间到QT,S空间之间的积分型算子是有意义的。本文给出了正规权Bloch空间到QT,S空间的积分型算子JhC的有界性和紧性成立的充分必要条件,以及CJh的有界性成立的充分必要条件。
参考文献/References:
[1]COWEN C C, CLUER M. Composition Operators on Spaces of Analytic Functions[M]. Boca Roton:CRC Press,1995.
[2]LI Songxiao, STEVIC′ S. Products of integral-type operator and composition operators between Bloch-type spaces[J]. Journal of Mathematical Analysis & Applications, 2009,349(2):596-610.
[3]WU Pengcheng, WULAN H. Composition operators from the Bloch space into the spaces QT[J]. International Journal of Mathematics & Mathematical Sciences, 2003,2003(31): 1973-1979.
[4]LOU Zengjian. Composition operators on Bloch type space[J].Analysis, 2003,1(1): 81-95.
[5]WULAN H. Compactness of composition operators from the Bloch space B to QK spaces[J].Acta Mathematica Sinica, 2005,21(6): 1415-1424.
[6]刘光荣,宋修朝,梁国宏. α-Bloch到正规权Bloch空间的复合算子[J]. 汕头大学学报(自然科学版), 2010, 25(4):12-17.
LIU Guangrong,SONG Xiuchao,LIANG Guohong.Composition operator from α-Bloch spaces to normal Bloch spaces[J]. Journal of Shantou University(Natural Science Edition), 2010, 25(4): 12-17.
[7]YANG Congli,XU Wen,KOTILAINEN M.Composition operators from Bloch type spaces into QK spaces[J].Journal of Mathamatical Analysis and Appllisations,2011,379(1):26-34.
[8]YONEDA R. Integration operators on weighted Bloch spaces[J]. Nihonkai Mathematical Journal, 2001,12(2):123-133.
[9]STEVIC′ S. Boundedness and compactness of an integral operator on a weighted space on the polydisc[J]. Indian Journal of Pure & Applied Mathematics, 2006,37(6):343.
[10]STEVIC′ S. Boundedness and compactness of an integral operator between H∞ and a mixed norm space on the polydisk[J]. Sibirsk Mat Zh, 2007,48(3):559-569.
[11]STEVIC′ S. On a new operator from the logarithmic Bloch space to the Bloch-type space on the unit ball[J]. Applied Mathematics and Computation, 2008,206(1):313-320.
[12]YU Yanyan,LIU Yongmin. Integral-type operators from weighted Bloch spaces into Bergman-type spaces[J]. Integral Transforms & Special Functions,2009, 20(6):419-428. [13]李海英, 田长安,张相波. 单位球上的加权Bergman空间到加权Bloch空间的积分型算子[J]. 数学杂志, 2012, 32(6): 1100-1104.
LI Haiying,TIAN Changan,ZHANG Xiangbo.Integral-type operators from weighted Bergman spaces to weighted Bloch spaces on the unit ball[J]. Journal of Mathematics, 2012, 32(6): 1100-1104.
[14]SHIELDS A L, WILLIAMS D L. Bounded projections,duality,and multipliers in spaces of analytic functions[J]. Transactions of the American Mathematical Society,1971,162:287-302.
[15]STEVIC S. Norm of weighted composition operators from Bloch space to H∞μ on the unit ball[J]. Ars combinatoria,2008,88:125-127.
[16]FU Xiaohong, ZHU Xiangling. Weighted composition operators on some weighted spaces in the unit ball[J]. Abstract and Applied Analysis,2008,605(3):807-814.
[17]WULAN H. Mobius invariant QP space:results,techniques and questions[J]. Advances in Mathematics(China), 2005,34(4): 385-403.
[18]WULAN H, WU Pengcheng. Characterizations of QT spaces[J]. Journal of Mathematical Analysis Applicatons, 2001,254(2): 484-497.
[19]周江河, 谭海鸥. 关于解析QT,S空间[J]. 五邑大学学报(自然科学版), 2009, 23(3): 50-52.
ZHOU Jianghe,TAN Haiou.On analytic QT,S spaces[J]. Journal of Wuyi University(Natural Science Edition), 2009, 23(3): 50-52.
[20]YANG Congli,XU Wen,KOTILAINEN M. Composition operators from Bloch type spaces into QK spaces[J]. Journal of Mathematical Analysis Applicatons,2011,379(1):26-34.