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Extended Cesàro Operators on Holomorphic Function Spaces in C~n

Author: ZhaoYanHui
Tutor: ZhangXueJun
School: Hunan Normal University
Course: Basic mathematics
Keywords: Cesàro Operator μ-Bloch space Dirichlet-type space Boundedness Compactness
CLC: O174.5
Type: Master's thesis
Year: 2006
Downloads: 15
Quote: 0
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Abstract


This thesis studies several holomorphic function space on the weighted the Cesàro operator , consists of four chapters . In the first chapter , we weighted Cesàro operator boundedness and compactness of the historical background and current situation are reviewed. Boundedness and compactness problem in the second chapter , we study the weighted Bloch type spaces on the polydisc Cesàro Operator , 0

g between the Bloch space and a small p -Bloch * < / sup > space ( p ≠ 0) is a bounded operator and compact operator . In the third chapter , we study the the C n unit ball in space to the β ν β μ , β μ 0 < / sub> the β ν 0 weighted Cesàro Operator boundedness and compactness the spatially weighted Cesàro the bounded and tight necessary and sufficient conditions are given . In the fourth chapter , we study the C n Dirichlet-type space on the unit ball D p μ the space β to μ-Bloch weighted Cesàro boundedness and compactness of the operator T g , T the g < / sub > β μ D p < / sub> bounded operator compact operator the necessary and sufficient conditions .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Complex analysis,complex function
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