| EXTENDED CESARO OPERATORS ON THE BLOCH SPACE IN THE UNIT BALL OF C^n |
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| 作者姓名： | 胡璋剑 |
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| 作者单位： | DepartmentolMathematics,HuzhouTeachersCollege,Huzhou313000,China |
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| 基金项目： | 浙江省自然科学基金 |
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| 摘 要： | The paper defines an extended Ceshro operator Tg with holomorphic symbol g in the unit ball B of C^n as Tg(f)(z) =∫^10f(tz)Rg(tz)dt/t, f∈H(B),z ∈ B. Where Rg(z) =∑^nj=1 zjθg/θzj is the radial derivative of g. In this paper, the author charac-terizes g for which Tg is bounded (or compact) on the Bloch space B and the little Bloch space B0.
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| 关 键 词： | 扩张Cesaro算子 Bloch空间 有界性 全纯函数 弱紧性 Gantmacher定理 |
EXTENDED CES(A)RO OPERATORS ON THE BLOCH SPACE IN THE UNIT BALL OF Cn |
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| Abstract: | The paper defines an extended Cesàro operator Tg with holomorphic symbolg in the unit ball B of Cn asWhere g(z)= ∑j=1∑n zj g/ zj is the radial derivative of g. In this paper, the author characterizes g for which Tg is bounded (or compact) on the Bloch spaceB and the little Blochspace B0. |
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| Keywords: | the Bloch space boundedness |
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