On the Boundedness of Singular Integrals in Morrey Spaces and its Preduals

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• 作者：Marcel Rosenthal ; Hans-Jürgen Schmeisser
• 关键词：Singular integral operators ; Calderón–Zygmund operators ; Morrey spaces ; Predual Morrey spaces
• 刊名：Journal of Fourier Analysis and Applications
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：22
• 期：2
• 页码：462-490
• 全文大小：819 KB
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• 作者单位：Marcel Rosenthal (1)
  Hans-Jürgen Schmeisser (1)
  
  1. Mathematisches Institut, Friedrich-Schiller-Universität Jena, 07737, Jena, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Fourier Analysis
  Abstract Harmonic Analysis
  Approximations and Expansions
  Partial Differential Equations
  Applications of Mathematics
  Signal,Image and Speech Processing
  
• 出版者：Birkh盲user Boston
• ISSN：1531-5851

文摘

We reduce the boundedness of operators in Morrey spaces \(L_p^r\left( {\mathbb R}^n\right) \), its preduals, \(H^{\varrho }L_p ({\mathbb R}^n)\), and their preduals \(\overset{\circ }{L}{}^r_{p}\left( \mathbb {R}^n\right) \) to the boundedness of the appropriate operators in Lebesgue spaces, \(L_p({\mathbb R}^n)\). Hereby, we need a weak condition with respect to the operators which is satisfied for a large set of classical operators of harmonic analysis including singular integral operators and the Hardy-Littlewood maximal function. The given vector-valued consideration of these issues is a key ingredient for various applications in harmonic analysis.