加權(quán)Bergman空間到加權(quán)Bloch空間的加權(quán)復(fù)合算子

鄒堃，譚海鷗

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加權(quán)Bergman空間到加權(quán)Bloch空間的加權(quán)復(fù)合算子

鄒堃，譚海鷗

（五邑大學(xué) 數(shù)學(xué)與計(jì)算科學(xué)學(xué)院，廣東 江門 529020）

加權(quán)Bergman空間；加權(quán)Bloch空間；加權(quán)復(fù)合算子；有界性；緊性

1 預(yù)備知識(shí)

2 主要定理及證明

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由式（1）知

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[1] ZHU Kehe. Operator theory in function spaces[M]. New York: Marcel Dekker Inc, 1990.

[2] ATTELE K R M. Toeplitz and Hankel operators on Bergman space[J]. Hokkaido Math, 1992, 329(2): 279-293.

[3] LI Songxiao. Weighted composition operators from Bergman spaces into weighted Bloch spaces[J]. Commun Korean Math Soc, 2005, 20(1): 63-77.

[4] HEDENMALM H, KORENBLUM B, ZHU Kehe. Theory of Bergman spaces[M]. New York:Springer Publishing, 2000.

[5] LI Songxiao. Volterra composition operators between weighted Bergman spaces and Bloch type spaces[J]. J Korean Math Soc, 2008, 45(1): 229-248.

[6] COWEN C C, MACCLUER B D. Composition operators on spaces of analytic functions[M]. Boca Raton: CRC Press, 1995.

[責(zé)任編輯：孫建平]

Weighted Composition Operators from Weighted Bergman Space into Weighted Bloch Space

ZOUKun,TANHai-ou

weighted Bergman space; weighted Bloch space; weighted composition operator; boundedness; compactness

1006-7302（2010）02-0004-46

O174.5；O177.2

A

2009-12-15

鄒堃（1982—），女，吉林樺甸人，碩士生，研究方向：復(fù)分析，E-mail: zoukun0411@163.com；譚海鷗，教授，碩士，碩士生導(dǎo)師，通信作者，主要從事復(fù)分析方面的研究，E-mail: Hotan@wyu.cn.