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Commutator Characterisation of Pseudo-differential Operators

  • Michael Ruzhansky
  • Ville Turunen
Part of the Pseudo-Differential Operators book series (PDO, volume 2)

Abstract

On a smooth closed manifold the pseudo-differential operators can be characterised by taking commutators with vector fields, i.e., first-order partial derivatives. This approach is due to Beals ([12], 1977), Dunau ([32], 1977), and Coifman and Meyer ([23], 1978); perhaps the first ones to consider these kind of commutator properties were Calderón and his school [21]. For other contributions, see also [26], [133] and [80].

Keywords

Sobolev Space Compact Manifold Closed Manifold Orientable Manifold Leibniz Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2010

Authors and Affiliations

  • Michael Ruzhansky
    • 1
  • Ville Turunen
    • 2
  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.Institute of MathematicsHelsinki University of TechnologyFinland

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