Singular integral operators with operator-valued kernels, and extrapolation of maximal regularity into rearrangement invariant Banach function spaces

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• 作者：Ralph Chill (1)
  Alberto Fiorenza (2) (3)
  
• 关键词：Primary 42B20 ; 34G10 ; Secondary 47D06 ; 46E30 ; Singular integral operator ; Calder脫n鈥揨ygmund operator ; Coifman鈥揊efferman inequality ; Rearrangement invariant Banachfunction space ; Boyd鈥檚 interpolation theorem ; Nonautonomous Cauchyproblem ; Maximal regularity ; Extrapolation ; Interpolation
• 刊名：Journal of Evolution Equations
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：14
• 期：4-5
• 页码：795-828
• 全文大小：378 KB
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• 作者单位：Ralph Chill (1)
  Alberto Fiorenza (2) (3)
  
  1. Fachrichtung Mathematik, Institut f眉r Analysis,, Technische Universit盲t Dresden, 01062, Dresden, Germany
  2. Dipartimento di Architettura, Universit谩 di Napoli, Via Monteoliveto, 3, 80134, Naples, Italy
  3. Istituto per le Applicazioni del Calcolo 鈥淢auro Picone鈥? sezione di Napoli, Consiglio Nazionale delle Ricerche, via Pietro Castellino, 111, 80131, Naples, Italy
  
• ISSN：1424-3202

文摘

We prove two extrapolation results for singular integral operators with operator-valued kernels, and we apply these results in order to obtain the following extrapolation of L p -maximal regularity: if an autonomous Cauchy problem on a Banach space has L p -maximal regularity for some \({p \in (1,\infty )}\) , then it has \({\mathbb{E}_w}\) -maximal regularity for every rearrangement invariant Banach function space \({\mathbb{E}}\) with Boyd indices \({1 and every Muckenhoupt weight \({w \in A_{p \mathbb{E}}}\) . We prove a similar result for nonautonomous Cauchy problems on the line.