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Boundedness of Pseudo-Differential Operators onLp, Sobolev and ModulationSpaces

Published online by Cambridge University Press:  28 January 2013

S. Molahajloo  and
G.E. Pfander
S. Molahajloo*
Affiliation:
Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L3N6, Canada
G.E. Pfander
Affiliation:
School of Engineering and Science, Jacobs University, 28759 Bremen, Germany
*
∗Corresponding author. E-mail: molahajloo@mast.queensu.ca
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Abstract

We introduce new classes of modulation spaces over phase space. By means of theKohn-Nirenberg correspondence, these spaces induce norms on pseudo-differential operatorsthat bound their operator norms on Lp–spaces,Sobolev spaces, and modulation spaces.

Keywords

pseudo-differential operatorsmodulation spacesSobolev spacesshort–time Fourier transforms
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 1: Harmonic analysis , 2013 , pp. 175 - 192
Copyright
© EDP Sciences, 2013

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