Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-26T20:46:56.929Z Has data issue: false hasContentIssue false
  • English
  • Français

Pseudo differential operators on local Hardy spaces on chébli-teimèche hypergroups

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Walter R. Bloom  and
Zengfu Xu
Walter R. Bloom
Affiliation:
Division of Science and Engineering Murdoch University Perth WA 6150 Australia e-mail: bloom@murdoch.edu.au
Zengfu Xu
Affiliation:
Division of Science and Engineering Murdoch University Perth WA 6150 Australia e-mail: zengfu@starwon.com.au
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we consider pseudo differential operators on local Hardy spaces hp (0 < p ≤ 1) on Chébli-Trimèche hypergroups of exponential growth.

Keywords

Pseudo differential operatorHardy spacehypergroup.

MSC classification

Secondary: 43A62: Hypergroups 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 43A32: Other transforms and operators of Fourier type
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 2 , April 2000 , pp. 202 - 230
Copyright
Copyright © Australian Mathematical Society 2000

References

[An]Anker, J.-Ph., ‘lp Fourier multipliers on Riemannian symmetric spaces of the noncompact type’, Ann. of Math. 132 (1990), 597–628.CrossRefGoogle Scholar
[AT]Achour, A. and Trimèche, K., ‘La g-fonction de Littlewood-Paley associée à un opérateur différentiel singulier sur (0, ∞)’, Ann. Inst. Fourier (Grenoble) 33 (1983), 203–226.CrossRefGoogle Scholar
[BH]Bloom, W. R. and Heyer, H., Harmonic analysis of probability measures on hypergroups, de Gruyter Studies in Math. 20 (de Gruyter, Berlin, 1995).CrossRefGoogle Scholar
[BX1]Bloom, W. R. and Xu, Z., ‘The Hardy-Littlewood maximal function for Chébli-Trimèche hypergroups’, in: Applications of hypergroups and related measure algebras (Joint Summer Research Conference, Seattle, 1993), Contemporary Math. 183 (Amer. Math. Soc., Providence, 1995) pp. 45–70.Google Scholar
[BX2]Bloom, W. R. and Xu, Z., ‘Maximal functions on Chébli-Trimèche hypergroups’, preprint.Google Scholar
[BX3]Bloom, W. R. and Xu, Z., ‘Fourier transforms of Schwartz functions on Chébli-Trimèche hypergroups’, Monatsh. Math. 125 (1998), 89–109.CrossRefGoogle Scholar
[BX4]Bloom, W. R. and Xu, Z., ‘Fourier multipliers for local Hardy spaces on Chébli-Trimèche hypergroups’, Canad. J. Math. 50 (1998), 897–928.CrossRefGoogle Scholar
[CV]Calderón, A. P. and Vaillancourt, R., ‘A class of bounded pseudo-differential operators’, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 1185–1187.CrossRefGoogle ScholarPubMed
[F]Fefferman, C., ‘lp bounds for pseudo-differential operators’, Israel J. Math. 14 (1973), 413–417.CrossRefGoogle Scholar
[G]Goldberg, D., ‘A local version of real Hardy space’, Duke Math. J. 46 (1979), 27–41.CrossRefGoogle Scholar
[H]Hörmander, L., Pseudo-differential operators and hypoelliptic equations, Proc. Sympos. Pure Math. 10 (Amer. Math. Soc., Providence, 1966), 138–183.Google Scholar
[K]Kawazoe, T., ‘Atomic Hardy spaces on semisimple Lie groups’, Japan. J. Math. 11 (1985), 293–343.Google Scholar
[PS]Päivärinta, L. and Somersalo, E., ‘A generalization of the Calderón-Vaillancourt theorem to L p and h p’, Math. Nachr. 138 (1988), 145–156.Google Scholar
[T1]Trimèche, K., ‘Transformation intégrale de Weyl et théorème de Paley-Wiener associés à un opérateur différentiel singulier sur (0, ∞)’, J. Math. Pures Appl.(9) 60 (1981), 51–98.Google Scholar
[T2]Trimèche, K., ‘Inversion of the lions transmutation operators using generalized wavelets’, Appl. Comput. Harmon. Anal. 4 (1997), 97–112.CrossRefGoogle Scholar