Manuscripta Mathematica

, Volume 144, Issue 3–4, pp 349–372 | Cite as

Pseudodifferential operators with non-regular operator-valued symbols

  • Bienvenido Barraza Martínez
  • Robert DenkEmail author
  • Jairo Hernández Monzón


In this paper, we consider pseudodifferential operators with operator-valued symbols and their mapping properties, without assumptions on the underlying Banach space E. We show that, under suitable parabolicity assumptions, the \({W_p^k(\mathbb{R}^n, E)}\)-realization of the operator generates an analytic semigroup. Our approach is based on oscillatory integrals and kernel estimates for them. An application to non-autonomous pseudodifferential Cauchy problems gives the existence and uniqueness of a classical solution. As an example, we include a discussion of coagulation–fragmentation processes.

Mathematics Subject Classification (2000)

35S05 47D06 35R20 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Bienvenido Barraza Martínez
    • 1
  • Robert Denk
    • 2
    Email author
  • Jairo Hernández Monzón
    • 1
  1. 1.Departamento de MatemáticasUniversidad del NorteBarranquillaColombia
  2. 2.Fachbereich MathematikUniversität KonstanzKonstanzGermany

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