VECTOR-VALUED THEOREM FOR THE UNCENTRED MAXIMAL OPERATOR ON BESSEL–KINGMAN HYPERGROUPS
Glasgow mathematical journal, Tome 56 (2014) no. 1, pp. 43-51

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.1017/S0017089513000050
Mots-clés : Primary 43A62, Secondary 43A15
DELEAVAL, LUC. VECTOR-VALUED THEOREM FOR THE UNCENTRED MAXIMAL OPERATOR ON BESSEL–KINGMAN HYPERGROUPS. Glasgow mathematical journal, Tome 56 (2014) no. 1, pp. 43-51. doi: 10.1017/S0017089513000050
@article{10_1017_S0017089513000050,
     author = {DELEAVAL, LUC},
     title = {VECTOR-VALUED {THEOREM} {FOR} {THE} {UNCENTRED} {MAXIMAL} {OPERATOR} {ON} {BESSEL{\textendash}KINGMAN} {HYPERGROUPS}},
     journal = {Glasgow mathematical journal},
     pages = {43--51},
     year = {2014},
     volume = {56},
     number = {1},
     doi = {10.1017/S0017089513000050},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000050/}
}
TY  - JOUR
AU  - DELEAVAL, LUC
TI  - VECTOR-VALUED THEOREM FOR THE UNCENTRED MAXIMAL OPERATOR ON BESSEL–KINGMAN HYPERGROUPS
JO  - Glasgow mathematical journal
PY  - 2014
SP  - 43
EP  - 51
VL  - 56
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000050/
DO  - 10.1017/S0017089513000050
ID  - 10_1017_S0017089513000050
ER  - 
%0 Journal Article
%A DELEAVAL, LUC
%T VECTOR-VALUED THEOREM FOR THE UNCENTRED MAXIMAL OPERATOR ON BESSEL–KINGMAN HYPERGROUPS
%J Glasgow mathematical journal
%D 2014
%P 43-51
%V 56
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000050/
%R 10.1017/S0017089513000050
%F 10_1017_S0017089513000050

[1] 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] 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] 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. Google Scholar | DOI

[4] 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] 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). Google Scholar | DOI

[6] 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] 7.Bloom, W. R. and Xu, Z., Fourier transforms of Schwartz functions on Chébli-Trimèche hypergroups, Monatsh. Math. 125 (2) (1998), 89–109. Google Scholar | DOI

[8] 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] 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. Google Scholar | DOI

[10] 10.Deleaval, L., Fefferman-Stein inequalities for the Dunkl maximal operator, J. Math. Anal. Appl. 360 (2) (2009), 711–726. Google Scholar | DOI

[11] 11.Fefferman, C. and Stein, E. M., Some maximal inequalities, Amer. J. Math. 93 (1971), 107–115. Google Scholar | DOI

[12] 12.Stein, E. M., Singular integrals and differentiability properties of functions (Princeton University Press, Princeton, NJ, 1970). Google Scholar

[13] 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] 14.Watson, G. N., A treatise on the theory of Bessel functions (Cambridge University Press, Cambridge, England, 1944). Google Scholar

[15] 15.Zeuner, H., One-dimensional hypergroups, Adv. Math. 76 (1) (1989), 1–18. Google Scholar | DOI

Cité par Sources :