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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The Weyl transform and $ L\sp p$ functions on phase space

Author: Barry Simon
Journal: Proc. Amer. Math. Soc. 116 (1992), 1045-1047
MSC: Primary 81S30; Secondary 47B38
MathSciNet review: 1100663
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Abstract: This is primarily a negative paper showing that a bound of the form $ \vert\vert W(f)\vert\vert{\text{operator norm}} \leq c\vert\vert f\vert{\vert _p}$ fails for the Weyl transform if $ p > 2$. $ {L^p}$ properties of Wigner distribution functions are discussed as well as Cwikel's theorem.

References [Enhancements On Off] (What's this?)

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  • [2] A. Klein and B. Russo, Sharp inequalities for Weyl operators and Heisenberg groups, Math. Ann. 235 (1978), 175-194. MR 0499945 (58:17687)
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  • [4] B. Simon, Trace ideals and their applications, Cambridge Univ. Press, Cambridge, 1979. MR 541149 (80k:47048)

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Article copyright: © Copyright 1992 American Mathematical Society

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