解析函数空间上的自伴加权复合算子Self-adjoint weighted composition operators on analytic functions spaces
江治杰;
摘要(Abstract)：
通过再生核函数刻画了Hardy空间,Bergman空间上自伴加权复合算子以及自伴等距加权复合算子,最后研究了单位球上的分式线性自同构,得到了一个充分条件。
关键词(KeyWords)： Hardy空间;Bergman空间;加权复合算子;自伴算子
基金项目(Foundation): 四川省青年基金(09ZC115);; 四川理工学院理学院科研项目
作者(Authors): 江治杰;
参考文献(References)：
- [1]Rudin W.Function Theory in the Unit Ball[M].New York:Spring-Verlag,1980.
- [2]Zhu K.Spaces of Holomorphic Functions in the Unit Ball[M].New York:Spring-Verlag,2007.
- [3]Cowen C C.An analytic Toeplitz operator that commutes with a compact operator and related class ofToeplitz operators[J].J.Funct.Anal.,1980,36(2):169-184.
- [4]Forelli F.The isometries of Hp[J].Canadian J.Math.,1964,16:721-728.
- [5]Contress M D,Hernandez-Diaz A G.Weighted composition operators on Hardy spaces[J].J.Math.Anal.Appl.,2001,263:224-231.
- [6]Choa J S,Ohno S.Product of composition and analytic Toeplitz operators[J].J.Math.Anal.Appl.,2003,281:320-332.
- [7]Contrerns M D,Hernandez-Diaz A G.Weighted composition operators between different Hardy spaces[J].Integral Equations Operator Theory,2003,46:165-188.
- [8]江治杰,柏宏斌.Hardy空间Hp(Bn)上的加权复合算子[J].数学进展,2008,37(6):749-754.
- [9]Cowen C C,MacCluer B D.Composition Operator on Space of Analytic Functions[M].Boca Raton:CRCPress,1995.
- [10]Bracci F.Linear fractional maps of unit ball[J].Advances in Mathematics,2002,167:265-287.
- [11]Cowen C C,MacCuler B.Linear fractional maps of unit ball and their composition operators[J].Acta.Sci.math(Szeged),2000,66:351-376.