Zygmund空间上的Volterra型算子与复合算子的乘积算子Products of Volterra Type Operator and Composition Operators on Z Space
林彩淑;叶善力;
摘要(Abstract)：
讨论了Zygmund空间上的Volterra型算子与复合算子的乘积算子的有界性和紧性,及小Zygmund空间Volterra型算子与复合算子的乘积算子的有界性和紧性,得到了CφI g(或I g Cφ)算子是Z空间与Z0空间上的有界算子与紧算子的充要条件.
关键词(KeyWords)： Volterra型算子;复合算子;Zygmund空间;有界性;紧性
基金项目(Foundation): 福建省省属高校专项基金资助项目(JK2012010)
作者(Authors): 林彩淑;叶善力;
参考文献(References)：
- [1]Zygmund A.Trigonometric series[M].London:Cambridge Press,1959.
- [2]Duren P.Theory of Hpspaces[M].New York:Academic Press,1970.
- [3]Cowen C C,Maccluer B D.Composition operator on spaces of analytic functions[M].Boca Raton:CRC Press,1995.
- [4]Ch Pommerenke.Schlichte funktionen und analytische Funktionen von beschrnkter mittlerer oszillation[J].Comment Math Helv,1977,52:591-602.
- [5]Benke G,Chang D C.A note on weighted Bergman spaces and the Cesro operator[J].Nagoya Math,2000,159:25-43.
- [6]Li Songxiao,Stevic S.Products of Volterra type operator and composition operator from H∞and Bloch spaces to Zygmund spaces[J].Math Anal Appl,2008,345(1):40-52.
- [7]Li S X,Stevic S.Volterra type operators ion operators on Zygmund spaces[J/OL].Journal of Inequalities and Applications,2007:0321242012-12-15〗.http://www.journal of inequalities and applications.com/content/2007/1/032124.
- [8]Siskakis A G,Zhao R.A Volterra type operator on spaces of analytic functions[J].Contemp Math,1999,232:299–311.
- [9]Ye Shanli,Hu Qingxiao.Weighted composition operators on the Zygmund space[J/OL].Abstract and Applied Analysis,2012:4624822012-12-15〗.http://www.hindawi.com/journals/aaa/2012/462482/.
- [10]Madigan K,Matheson A.Compact composition operators on the Bloch space[J].Trans Amer Math Soc,1995,347(7):2679-2687.
- [11]Li S,Stevic S.Gerneralized composition operators on the Zygmund spaces and Bloch type spaces[J].Math Anal Appl,2008,338:1282-1295.