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Fourier Multipliers For Local Hardy Spaces On Chébli-Trimèche Hypergroups

Published online by Cambridge University Press:  20 November 2018

Walter R. Bloom  and
Zengfu Xu
Walter R. Bloom
Affiliation:
Division of Science, Murdoch University, Perth, WA 6150, Australia email: bloom@murdoch.edu.au, engfu@murdoch.edu.au
Zengfu Xu
Affiliation:
Division of Science, Murdoch University, Perth, WA 6150, Australia email: bloom@murdoch.edu.au, engfu@murdoch.edu.au
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Abstract

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In this paper we consider Fourier multipliers on local Hardy spaces ${{\mathbf{h}}^{\mathbf{p}}}(0<p\le 1)$ for Chébli-Trimèche hypergroups. The molecular characterization is investigated which allows us to prove a version of Hörmander’s multiplier theorem.

Keywords

43A6243A1543A32Fourier multipliersHardy spaceshypergroup
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 5 , 01 October 1998 , pp. 897 - 928
Copyright
Copyright © Canadian Mathematical Society 1998

References

[Al] Alexopoulos, G., Spectral multipliers on Lie groups of polynomial growth. Proc. Amer. Math. Soc. 120(1994), 973–979.Google Scholar
[An] J-Ph. Anker, Lp Fourier multipliers on Riemannian symmetric spaces of the noncompact type. Ann. of Math 132(1990), 597–628.Google Scholar
[AT] Achour, A. and Trimèche, K., La g-fonction de Littlewood-Paley associée à un opérateur différentiel singulier sur. (0,1). Ann. Inst. Fourier (Grenoble) 33(1983), 203–226.Google Scholar
[BH] Bloom, W.R. and Heyer, H., Harmonic analysis of probability measures on hypergroups. de Gruyter Studies in Math. 20, Walter de Gruyter, Berlin, New York, 1995.Google Scholar
[BX1] Bloom, W.R. and Xu, Z., The Hardy-Littlewood maximal function for Chébli-Trimèche hypergroups. Applications of hypergroups and related measure algebras, Joint Summer Research Conference, Seattle, 1993. 45–70, Contemporary Math. 183, Amer. Math. Soc., Providence, Rhode Island, 1995.Google Scholar
[BX2] Bloom, W.R., Local Hardy spaces on Chébli-Trimèche hypergroups. preprint.Google Scholar
[BX3] Bloom, W.R., Fourier multipliers for Lp (p > 1) on Chébli-Trimèche hypergroups. preprint.+1)+on+Chébli-Trimèche+hypergroups.+preprint.>Google Scholar
[BX4] Bloom, W.R., Fourier transforms of functions in Schwartz spaces on Chébli-Trimèche hypergroups. Monatsh. Math. 125(1998), 89–109.Google Scholar
[C] Chébli, H., Sur un théorème de Paley-Wiener associé à la décomposition spectrale d’un opérateur de Sturm-Liouville sur ]0,∞[. J. Funct. Anal. 17(1974), 447–461.Google Scholar
[CS] Clerc, J.-L. and Stein, E.M., Lp multipliers for noncompact symmetric spaces. Proc.Nat.Acad. Sci.U.S.A. 71(1974), 3911.ndash;3912.Google Scholar
[CW] Coifman, R. and G.Weiss, Extensions of Hardy spaces and their use in analysis. Bull. Amer.Math. Soc. 83(1977), 549–645.Google Scholar
[FS] Folland, G.B. and Stein, E.M., Hardy spaces on homogeneous groups. Math. Notes 28, Princeton Univ. Press, 1982.Google Scholar
[FX] Fan, D. and Xu, Z., Hp estimates for bi-invariant operators on compact Lie groups. Proc. Amer. Math. Soc. 122(1994), 437–447.Google Scholar
[K] Kawazoe, T., Atomic Hardy spaces on semisimple Lie groups. Japan. J. Math. 11(1985), 293–343.Google Scholar
[S] Stempak, K., La théorie de Littlewood-Paley pour la transformation de Fourier-Bessel. C. R. Acad. Sci. Paris Sér I, Math. 303(1986), 15–18.Google Scholar
[ST] Stanton, R.J. and Thomas, P.A., Expansions for spherical functions on noncompact symmetric spaces. Acta Math. 140(1978), 251–276.Google Scholar
[T] Trimèche, K., Transformation intégrale de Weyl et théorème de Paley-Wiener associés à un opérateur différentiel singulier sur. (0,1). J. Math. Pures Appl. (9) 60(1981), 51–98.Google Scholar
[TW] Taibleson, M. and Weiss, G., The molecular characterization of certain Hardy spaces. Astérisque 77(1980), 67–151.Google Scholar
[W] Weiss, N.J., Lp-estimates for bi-invariant operators on compact Lie groups. Amer. J. Math. 94(1972), 103–118.Google Scholar