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Pseudo-Differential Operators with Symbols in Modulation Spaces

  • Joachim Toft
Part of the Operator Theory: Advances and Applications book series (OT, volume 205)

Abstract

We establish continuity results for pseudo-differential operators with symbols in modulation spaces. Especially it follows from our general result that if aW ∞,1(R 2d ), then the pseudo-differential operator a(x, D) is continuous from M ∞,1(R d ) to W ∞,1(R d). If instead aW ∞,1(R 2d ), then it follows that a(x, D) is continuous from M 1,∞(R d ) to W 1,∞(R d ).

Keywords

Modulation spaces Wiener amalgam spaces pseudo-differential operators 

Mathematics Subject Classification (2000)

Primary 35S05 42B35 44A35 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Joachim Toft
    • 1
  1. 1.Department of Mathematics and Systems EngineeringVäxjö UniversitySweden

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