Poletsky–Stessin Hardy Spaces on Complex Ellipsoids in \(\mathbb {C}^{n}\)

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• 作者：Sibel Şahin
• 关键词：Hardy space ; Complex ellipsoid ; Approach region ; Composition operator ; Primary 32C15 ; Secondary 47B33
• 刊名：Complex Analysis and Operator Theory
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：10
• 期：2
• 页码：295-309
• 全文大小：471 KB
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• 作者单位：Sibel Şahin (1)
  
  1. Sabancı University, Tuzla, 34956, Istanbul, Turkey
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Operator Theory
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1661-8262

文摘

We study Poletsky–Stessin Hardy spaces on complex ellipsoids in \(\mathbb {C}^{n}\). Different from one variable case, classical Hardy spaces are strictly contained in Poletsky–Stessin Hardy spaces on complex ellipsoids so boundary values are not automatically obtained in this case. We have showed that functions belonging to Poletsky–Stessin Hardy spaces have boundary values and they can be approached through admissible approach regions in the complex ellipsoid case. Moreover, we have obtained that polynomials are dense in these spaces. We also considered the composition operators acting on Poletsky–Stessin Hardy spaces on complex ellipsoids and gave conditions for their boundedness and compactness. Keywords Hardy space Complex ellipsoid Approach region Composition operator