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A class of logarithmic Hardy-Bloch type spaces and operator

Author: WuXiaoMing
Tutor: YeShanLi
School: Fujian Normal University
Course: Basic mathematics
Keywords: Hardy hurried Space Dirichlet Space ( ? ) Space VMOA space Taylor coefficients Weighted Composition Operators
CLC: O174.5
Type: Master's thesis
Year: 2010
Downloads: 7
Quote: 0
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Abstract


This paper is the study of the complex plane Hardy spaces on the unit disk based on the study of two new spaces : Logarithmic Hardy-Bloch type spaces (DHαLp) and small logarithmic Hardy-Bloch type spaces (DHαLp, 0). And investigate some properties of these two spaces , as follows : The first chapter briefly describes Hardy Spaces research , which lists some of the main conclusions of this paper ; introduce some space, composition operators and weighted composition operators concept. second chapter focuses on when α = 1时, DHLp and Hardy spaces (Hp), Dirichlet type spaces ((?) pp1) and VMOA spatial containment relationship , given f ∈ DHLp a characterization of the growth rate when the α gt; 1时, are given f ∈ DHαLp (DHαLp, 0). 's a necessary and sufficient condition for any while α ≥ 1, the estimated f (z) = (?) DHαLp (DHαLp, 0) in αn with n changes . Chapter III studies when α = 1时, DHLp space respectively to Bloch space and little Bloch space weighted Composition Operators boundedness and compactness of a sufficient condition and a necessary condition were given space to the Bloch space DHLp Bloch spaces and small composite operator boundedness and compactness of a necessary and sufficient condition .

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