Proceedings of the American Mathematical Society

Author(s): Jay Epperson
Journal: Proc. Amer. Math. Soc. 124 (1996), 2061-2068.
MSC (1991): Primary 42C10
Retrieve article in: PDF
This article is available free of charge

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.

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

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 42C10

Jay Epperson
Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131
Email: jeppers@math.unm.edu

DOI: 10.1090/S0002-9939-96-03486-7
PII: S 0002-9939(96)03486-7
Received by editor(s): January 3, 1995
Communicated by: J. Marshall Ash
Copyright of article: Copyright 1996, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS