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Proceedings of the American Mathematical Society

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Hermite multipliers and pseudo-multipliers

Author: Jay Epperson
Journal: Proc. Amer. Math. Soc. 124 (1996), 2061-2068
MSC (1991): Primary 42C10
MathSciNet review: 1343690
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Abstract: We prove a multiplier theorem for the Hermite-Triebel-Lizorkin spaces introduced by Epperson in [Studia Math. 114 (1995), 87--103]. This extends Thangavelu's theorem [Revist. Mat. Ibero 3 (1987), 1--24; Math. Notes, vol. 42, 1993] on Hermite multipliers for $L^p$ spaces. We also prove an $L^p$ boundedness result for a class of Hermite pseudo-multipliers.

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Jay Epperson
Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131

Received by editor(s): January 3, 1995
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society