Integral Operators, Embedding Theorems and a Littlewood–Paley Formula on Weighted Fock Spaces

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• 作者：Olivia Constantin ; José Ángel Peláez
• 关键词：Fock spaces ; Integral operators ; Carleson measures ; Littlewood–Paley formula ; Invariant subspaces
• 刊名：Journal of Geometric Analysis
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：26
• 期：2
• 页码：1109-1154
• 全文大小：749 KB
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• 作者单位：Olivia Constantin (1)
  José Ángel Peláez (2)
  
  1. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria
  2. Departamento de Analisis Matematico, Universidad de Malaga, Campus de Teatinos, 29071, Malaga, Spain
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X

文摘

We obtain a complete characterization of the entire functions \(g\) such that the integral operator \((T_ g f)(z)=\int _{0}^{z}f(\zeta )\,g'(\zeta )\,d\zeta \) is bounded or compact, on a large class of Fock spaces \({\mathcal {F}}^\phi _p\), induced by smooth radial weights that decay faster than the classical Gaussian one. In some respects, these spaces turn out to be significantly different from the classical Fock spaces. Descriptions of Schatten class integral operators are also provided. En route, we prove a Littlewood–Paley formula for \(||\cdot ||_{{\mathcal {F}}^\phi _p}\) and we characterize the positive Borel measures for which \({\mathcal {F}}^\phi _p\subset L^q(\mu )\), \(0<p,q<\infty \). In addition, we also address the question of describing the subspaces of \({\mathcal {F}}^\phi _p\) that are invariant under the classical Volterra integral operator.