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

Author(s): Mitsuru Sugimoto; Naohito Tomita
Journal: Proc. Amer. Math. Soc. 136 (2008), 1681-1690.
MSC (2000): Primary 42B35, 47G30
Posted: January 17, 2008
MathSciNet review: 2373597
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Abstract | References | Similar articles | Additional information

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 $M^{p,q}$ ( $q\neq2$ ).

References:

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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: 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
Posted: January 17, 2008
Communicated by: Michael T. Lacey
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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