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VECTOR-VALUED THEOREM FOR THE UNCENTRED MAXIMAL OPERATOR ON BESSEL–KINGMAN HYPERGROUPS

Published online by Cambridge University Press:  13 August 2013

LUC DELEAVAL
LUC DELEAVAL*
Affiliation:
Laboratoire d'Analyse et de Mathématiques Appliquées, Université Paris-Est Marne la Vallée, 5 Boulevard Descartes, Champs sur Marne, Marne la Vallée 77454, Cédex 2, France e-mail: luc.deleaval@univ-mlv.fr
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Abstract

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In this paper we introduce a vector-valued uncentred maximal operator in the setting of one-dimensional Bessel–Kingman hypergoups, and prove a maximal theorem for it.

Keywords

Primary 43A62Secondary 43A15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 1 , January 2014 , pp. 43 - 51
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

REFERENCES

1.Achour, A. and Trimèche, K., La g-fonction de Littlewood-Paley associée à un opérateur différentiel singulier sur (0, ∞), Ann. Inst. Fourier (Grenoble) 33 (4) (1983), 203–226.Google Scholar
2.Andrews, G. E., Askey, R. and Roy, R., Special functions, Encyclopedia of Mathematics and its Applications, vol. 71 (Cambridge University Press, Cambridge, UK, 1999).Google Scholar
3.Betancor, J. J., Betancor, J. D. and Méndez, J. M., Distributional Fourier transform and convolution associated to Chébli-Trimèche hypergroups, Monatsh. Math. 134 (4) (2002), 265–286.CrossRefGoogle Scholar
4.Betancor, J. D., Betancor, J. J. and Méndez, J. M. R., Convolution operators on Schwartz spaces for Chébli-Trimèche hypergroups, Rocky Mountain J. Math. 37 (3) (2007), 723–761.Google Scholar
5.Bloom, W. R. and Heyer, H., Harmonic analysis of probability measures on hypergroups, de Gruyter Studies in Mathematics, vol. 20 (Walter de Gruyter, Berlin, Germany, 1995).CrossRefGoogle Scholar
6.Bloom, W. R. and Xu, Z. F., The Hardy–Littlewood maximal function for Chébli-Trimèche hypergroups. In Applications of hypergroups and related measure algebras (a Joint Summer Research Conference on Applications of Hypergroups and Related Measure Algebras, 31 July–6 August 1993, Seattle, Washington, Contemporary Mathematics, vol. 183. (American Mathematical Society, Providence, RI, 1995), 45–70.Google Scholar
7.Bloom, W. R. and Xu, Z., Fourier transforms of Schwartz functions on Chébli-Trimèche hypergroups, Monatsh. Math. 125 (2) (1998), 89–109.CrossRefGoogle Scholar
8.Bloom, W. R. and Xu, Z., Fourier multipliers for Lp on Chébli-Trimèche hypergroups, Proc. Lond. Math. Soc. 80 (3) (2000), 643–664.Google Scholar
9.Bloom, W. R. and Xu, Z., Maximal functions on Chébli-Trimèche hypergroups, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 3 (3) (2000), 403–434.CrossRefGoogle Scholar
10.Deleaval, L., Fefferman-Stein inequalities for the ${\mathbb Z}^d_2$ Dunkl maximal operator, J. Math. Anal. Appl. 360 (2) (2009), 711–726.CrossRefGoogle Scholar
11.Fefferman, C. and Stein, E. M., Some maximal inequalities, Amer. J. Math. 93 (1971), 107–115.CrossRefGoogle Scholar
12.Stein, E. M., Singular integrals and differentiability properties of functions (Princeton University Press, Princeton, NJ, 1970).Google Scholar
13.Stempak, K., La théorie de Littlewood-Paley pour la transformation de Fourier-Bessel, C. R. Acad. Sci. Paris Sér. I Math. 303 (1) (1986), 15–18.Google Scholar
14.Watson, G. N., A treatise on the theory of Bessel functions (Cambridge University Press, Cambridge, England, 1944).Google Scholar
15.Zeuner, H., One-dimensional hypergroups, Adv. Math. 76 (1) (1989), 1–18.CrossRefGoogle Scholar