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Pseudo-Differential Operators and Schatten-von Neumann Classes

  • Ernesto Buzano
  • Fabio Nicola
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 155)

Abstract

For a Hörmander’s symbol classS(m g)it is proved that the weight m is in L p (ℝ2n , with 1 ⩽ p ⩽ ∞ if and only if all pseudo-differential operators with Weyl symbol inS(m g)are in the Schatten-von Neumann class Sp (L2).

Mathematics Subject Classification (2000).Primary 47B10; Secondary 35S05.

Keywords

Schatten-von Neumann classes hypoellipticity pseudo-differential operators Weyl-Hörmander calculus 

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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Ernesto Buzano
    • 1
  • Fabio Nicola
    • 1
  1. 1.Dipartimento di MatematicaUniversità di TorinoTorinoItaly

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