Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Hermite multipliers and pseudo-multipliers

Author(s): 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.

References:

1.: J. Epperson, Triebel-Lizorkin spaces for Hermite expansions, Studia Math. 114 (1995), 87--103.
2.: S.G. Mihlin, On the multipliers of Fourier integrals, Dokl. Acad. Nauk SSSR N.S. 109 (1956), 701--703 (Russian). MR 18:304a
3.: B. Muckenhoupt, Mean convergence of Hermite and Laguerre series II, Trans. Amer. Math. Soc. 147 (1970), 433-460. MR 41:711
4.: E.M. Stein, Harmonic Analysis, Princeton University Press, 1993. MR 95c:42002
5.: S. Thangavelu, Multipliers for Hermite expansions, Revist. Mat. Ibero. 3 (1987), 1--24. MR 90h:42043
6.: S. Thangavelu, Lectures on Hermite and Laguerre Expansions, Mathematical Notes 42, Princeton University Press, 1993. MR 94i:42001
7.: H. Triebel, Theory of Function Spaces, Birkhäuser Verlag, Basel (Monographs in Mathematics, Vol. 78), 1983. MR 86j:46026
8.: H. Triebel, Theory of Function Spaces II, Birkhäuser Verlag, Basel (Monographs in Mathematics, Vol. 84), 1992. MR 93f:46029

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