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

Sugimoto, Mitsuru; Tomita, Naohito

doi:10.1090/S0002-9939-08-09253-8

A counterexample for boundedness of pseudo-differential operators on modulation spaces
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by Mitsuru Sugimoto and Naohito Tomita PDF

Proc. Amer. Math. Soc. 136 (2008), 1681-1690 Request permission

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 $M^{p,q}$ ($q\neq 2$).

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