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Boundedness of Pseudo-Differential Operators on Hörmander Spaces

  • G. M. Iancu
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 5)

Abstract

We prove the boundedness of a class of pseudo-differential operators on the Hörmander spaces \({\dot H^{0,p}},1 < p < \infty .\) Examples are given to show that the classical pseudo-differential operators fail to be bounded on these spaces. Fourier integral operators and their global mapping properties are studied in this setting. Applications to the regularity of solutions of semilinear pseudo-differential equations on ℝn are presented.

Keywords

Asymptotic Expansion Bounded Linear Operator Besov Space Pseudodifferential Operator Schwartz Space 
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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • G. M. Iancu
    • 1
  1. 1.Department of Mathematics and StatisticsYork UniversityNorth YorkCanada

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