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Mapping properties for operator-valued pseudodifferential operators on toroidal Besov spaces

  • B. Barraza Martínez
  • R. Denk
  • J. Hernández Monzón
  • M. Nendel
Article
  • 85 Downloads

Abstract

In this paper, we consider pseudodifferential operators on the torus with operator-valued symbols and prove continuity properties on vector-valued toroidal Besov spaces, without assumptions on the underlying Banach spaces. The symbols are of limited smoothness with respect to x and satisfy a finite number of estimates on the discrete derivatives. The proof of the main result is based on a description of the operator as a convolution operator with a kernel representation which is related to the dyadic decomposition appearing in the definition of the Besov space.

Keywords

Pseudodifferential operators Vector-valued Besov spaces Convolution kernels 

Mathematics Subject Classification

35S05 47D06 35R20 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad del NorteBarranquillaColombia
  2. 2.Fachbereich für Mathematik und StatistikUniversity of KonstanzKonstanzGermany

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