Coefficients Multipliers of Weighted Spaces of Harmonic Functions

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• 作者：Kjersti Solberg Eikrem ; Eugenia Malinnikova
• 关键词：42B15 ; 46E15 ; 47B38 ; Weighted spaces of harmonic functions ; Cesàro means ; multipliers ; spherical harmonics ; doubling weight
• 刊名：Integral Equations and Operator Theory
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：82
• 期：4
• 页码：555-573
• 全文大小：589 KB
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• 作者单位：Kjersti Solberg Eikrem (1)
  Eugenia Malinnikova (1)
  
  1. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8989

文摘

Let \({h_g^\infty}\) be the space of harmonic functions in the unit ball that are bounded by some increasing radial function that tends to infinity as r goes to one; these spaces are called growth spaces. We describe functions in growth spaces by the Cesàro means of their expansions in harmonic polynomials and apply this characterization to study coefficient multipliers between growth spaces. Further, we introduce spaces of harmonic functions of regular growth and show that integral operators considered recently in connection to boundary oscillation of harmonic functions in weighted spaces, can be realized as multipliers that map growth spaces to corresponding spaces of regular growth.