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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A counterexample for boundedness of pseudo-differential operators on modulation spaces


Authors: Mitsuru Sugimoto and Naohito Tomita
Journal: Proc. Amer. Math. Soc. 136 (2008), 1681-1690
MSC (2000): Primary 42B35, 47G30
Published electronically: January 17, 2008
MathSciNet review: 2373597
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Abstract: We prove that pseudo-differential operators with symbols in the class $ S_{1,\delta}^0$ ( $ 0<\delta<1$) are not always bounded on the modulation space $ M^{p,q}$ ($ q\neq2$).


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Additional Information

Mitsuru Sugimoto
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
Email: sugimoto@math.sci.osaka-u.ac.jp

Naohito Tomita
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
Email: tomita@gaia.math.wani.osaka-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09253-8
PII: S 0002-9939(08)09253-8
Keywords: Modulation spaces, pseudo-differential operators
Received by editor(s): January 4, 2007
Published electronically: January 17, 2008
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.