C. Abdelkefi and M. Sifi, Dunkl Translation and Uncentered Maximal Operator on the Real Line, International Journal of Mathematics and Mathematical Sciences, vol.123, issue.1, 2007.
DOI : 10.1016/j.jfa.2003.11.009

A. Achour and K. Trimèche, La $g$-fonction de Littlewood-Paley associ??e ?? un op??rateur diff??rentiel singulier sur $(0,\infty)$, Annales de l???institut Fourier, vol.33, issue.4, pp.203-226, 1983.
DOI : 10.5802/aif.946

URL : http://www.numdam.org/article/AIF_1983__33_4_203_0.pdf

B. Amri, J. Anker, and M. Sifi, Three results in Dunkl analysis, Colloquium Mathematicum, vol.118, issue.1, pp.299-312, 2010.
DOI : 10.4064/cm118-1-16

G. E. Andrews, R. Askey, and R. Roy, Special functions, volume 71 of Encyclopedia of Mathematics and its Applications, 1999.

T. H. Baker and P. J. Forrester, The Calogero-Sutherland Model and Generalized Classical Polynomials, Communications in Mathematical Physics, vol.188, issue.1, pp.175-216, 1997.
DOI : 10.1007/s002200050161

T. H. Baker and P. J. Forrester, Nonsymmetric Jack polynomials and integral kernels, Duke Mathematical Journal, vol.95, issue.1, pp.1-50, 1998.
DOI : 10.1215/S0012-7094-98-09501-1

URL : http://arxiv.org/abs/q-alg/9612003

R. Walter, H. Bloom, and . Heyer, Harmonic analysis of probability measures on hypergroups, 1995.

R. Walter, Z. Bloom, and . Xu, The Hardy-Littlewood maximal function for Chébli-Trimèche hypergroups In Applications of hypergroups and related measure algebras, Contemp. Math, vol.183, pp.45-70, 1993.

R. Walter, Z. Bloom, and . Xu, Maximal functions on Chébli-Trimèche hypergroups, Infin. Dimens. Anal. Quantum Probab. Relat. Top, vol.3, issue.3, pp.403-434, 2000.

J. Marcel-de, The Dunkl transform, Invent. Math, vol.113, issue.1, pp.147-162, 1993.

J. Marcel-de, Paley-Wiener theorems for the Dunkl transform, Trans. Amer. Math. Soc, vol.358, issue.10, pp.4225-4250, 2006.

L. Deleaval, Fefferman-Stein inequalities for the Z d 2 Dunkl maximal operator, J
URL : https://hal.archives-ouvertes.fr/hal-00333258

N. Demni, Generalized Bessel function of type D. SIGMA Symmetry Integrability Geom, Methods Appl, vol.7, 2008.

N. Dunford, J. T. Schwartz, W. G. Bade, and R. G. Bartle, Linear Operators. I. General Theory. With the assistance of, Pure and Applied Mathematics, vol.7, 1958.

C. F. Dunkl, The measure algebra of a locally compact hypergroup, Transactions of the American Mathematical Society, vol.179, pp.331-348, 1973.
DOI : 10.1090/S0002-9947-1973-0320635-2

C. F. Dunkl, Differential-difference operators associated to reflection groups, Transactions of the American Mathematical Society, vol.311, issue.1, pp.167-183, 1989.
DOI : 10.1090/S0002-9947-1989-0951883-8

C. F. Dunkl, Operators commuting with Coxeter group actions on polynomials, Invariant theory and tableaux, pp.107-117, 1988.

C. F. Dunkl, Integral kernels with reflection group invariance. Canad, J. Math, vol.43, issue.6, pp.1213-1227, 1991.
DOI : 10.4153/cjm-1991-069-8

C. F. Dunkl, Hankel transforms associated to finite reflection groups, Hypergeometric functions on domains of positivity, Jack polynomials, and applications, pp.123-138, 1991.
DOI : 10.1090/conm/138/1199124

C. F. Dunkl, Intertwining Operators Associated to the Group S 3, Transactions of the American Mathematical Society, vol.347, issue.9, pp.3347-3374, 1995.
DOI : 10.2307/2155014

C. F. Dunkl, AN INTERTWINING OPERATOR FOR THE GROUP B2, Glasgow Mathematical Journal, vol.49, issue.02, pp.291-319, 2007.
DOI : 10.1215/S0012-7094-99-09813-7

C. F. Dunkl, M. De-jeu, and E. M. Opdam, Singular polynomials for finite reflection groups, Transactions of the American Mathematical Society, vol.346, issue.1, pp.237-256, 1994.
DOI : 10.1090/S0002-9947-1994-1273532-6

F. Charles, Y. Dunkl, and . Xu, Orthogonal polynomials of several variables, volume 81 of Encyclopedia of Mathematics and its Applications, 2001.

C. Fefferman and E. M. Stein, Some Maximal Inequalities, American Journal of Mathematics, vol.93, issue.1, pp.107-115, 1971.
DOI : 10.2307/2373450

M. Flensted-jensen and T. Koornwinder, The convolution structure for Jacobi function expansions, Arkiv f??r Matematik, vol.11, issue.1-2, pp.245-262, 1973.
DOI : 10.1007/BF02388521

L. Gallardo and L. Godefroy, Un principe d'invariance relatif ?? un processus g??n??ralisant le mouvement brownien N-dimensionnel, Comptes Rendus Mathematique, vol.338, issue.6, pp.487-492, 2004.
DOI : 10.1016/j.crma.2004.01.016

G. H. Hardy and J. E. Littlewood, A maximal theorem with function-theoretic applications, Acta Mathematica, vol.54, issue.0, pp.81-116, 1930.
DOI : 10.1007/BF02547518

G. J. Heckman, Dunkl operators Astérisque, Séminaire Bourbaki, vol.4, issue.245 828, pp.223-24697, 1996.

J. E. Humphreys, Reflection groups and Coxeter groups, volume 29 of Cambridge Studies in Advanced Mathematics, 1990.

R. I. Jewett, Spaces with an abstract convolution of measures, Advances in Mathematics, vol.18, issue.1, pp.1-101, 1975.
DOI : 10.1016/0001-8708(75)90002-X

R. Kane, Reflection groups and invariant theory, CMS Books in Mathematics, vol.5, 2001.
DOI : 10.1007/978-1-4757-3542-0

M. Lassalle, Polynômes de Jacobi généralisés, C. R. Acad. Sci. Paris Sér. I Math, vol.312, issue.6, pp.425-428, 1991.

I. G. Macdonald, Symmetric functions and Hall polynomials Oxford Mathematical Monographs, 1995.

M. Maslouhi and E. H. Youssfi, The Dunkl intertwining operator, Journal of Functional Analysis, vol.256, issue.8, pp.2697-2709, 2009.
DOI : 10.1016/j.jfa.2008.09.018

E. Michael, Topologies on spaces of subsets, Transactions of the American Mathematical Society, vol.71, issue.1, pp.152-182, 1951.
DOI : 10.1090/S0002-9947-1951-0042109-4

A. Nowak, L. Roncal, and K. Stempak, Riesz transforms for the Dunkl Ornstein???Uhlenbeck operator, Colloquium Mathematicum, vol.118, issue.2, pp.669-684, 2010.
DOI : 10.4064/cm118-2-19

A. Nowak and K. Stempak, Riesz transforms for the Dunkl harmonic oscillator, Mathematische Zeitschrift, vol.202, issue.3, pp.539-556, 2009.
DOI : 10.1007/s00209-008-0388-4

E. M. Opdam, Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group, Compositio Math, vol.85, issue.3, pp.333-373, 1993.

M. Rösler, Bessel-type signed hypergroups on R. In Probability measures on groups and related structures, XI (Oberwolfach, World Sci. Publ, pp.292-304, 1994.

M. Rösler, Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators, Communications in Mathematical Physics, vol.192, issue.3, pp.519-542, 1998.
DOI : 10.1007/s002200050307

M. Rösler, Positivity of Dunkl's intertwining operator. Duke Math, J, vol.98, issue.3, pp.445-463, 1999.

M. Rösler, One-parameter semigroups related to abstract quantum models of Calogero type, Infinite dimensional harmonic analysis, pp.290-305, 1999.

M. Rösler, Dunkl Operators: Theory and Applications, Orthogonal polynomials and special functions, pp.93-135, 2002.
DOI : 10.1007/3-540-44945-0_3

M. Rösler, A positive radial product formula for the Dunkl kernel, Transactions of the American Mathematical Society, vol.355, issue.06, pp.2413-2438, 2003.
DOI : 10.1090/S0002-9947-03-03235-5

M. Rösler and M. Voit, Markov Processes Related with Dunkl Operators, Advances in Applied Mathematics, vol.21, issue.4, pp.575-643, 1998.
DOI : 10.1006/aama.1998.0609

R. Spector, Mesures invariantes sur les hypergroupes, Transactions of the American Mathematical Society, vol.239, pp.147-165, 1978.
DOI : 10.1090/S0002-9947-1978-0463806-1

R. P. Stanley, Some combinatorial properties of Jack symmetric functions, Advances in Mathematics, vol.77, issue.1, pp.76-115, 1989.
DOI : 10.1016/0001-8708(89)90015-7

URL : http://doi.org/10.1016/0001-8708(89)90015-7

E. M. Stein and J. Strömberg, Behavior of maximal functios in Rn for large n, Arkiv f??r Matematik, vol.21, issue.1-2, pp.259-269, 1983.
DOI : 10.1007/BF02384314

M. Elias and . Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, issue.30, 1970.

M. Elias and . Stein, Topics in harmonic analysis related to the Littlewood-Paley theory, Annals of Mathematics Studies, issue.63, 1970.

M. Elias and . Stein, Harmonic analysis : real-variable methods, orthogonality, and oscillatory integrals, volume 43 of Princeton Mathematical Series, 1993.

M. Elias, G. Stein, and N. J. Weiss, Introduction to Fourier analysis on Euclidean spaces, 1971.

K. Stempak, La théorie de Littlewood-Paley pour la transformation de Fourier-Bessel, C. R. Acad. Sci. Paris Sér. I Math, vol.303, issue.1, pp.15-18, 1986.

J. Strömberg, Weak Type L 1 Estimates for Maximal Functions on Non-Compact Symmetric Spaces, The Annals of Mathematics, vol.114, issue.1, pp.115-126, 1981.
DOI : 10.2307/1971380

G. Szeg? and R. I. , Orthogonal polynomials, 1967.
DOI : 10.1090/coll/023

S. Thangavelu and Y. Xu, Convolution operator and maximal function for the Dunkl transform, Journal d'Analyse Math??matique, vol.29, issue.1, pp.25-55, 2005.
DOI : 10.1007/BF02807401

K. Trimèche, Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators, Integral Transforms and Special Functions, vol.13, issue.1, pp.17-38, 2002.
DOI : 10.1080/10652460212888

G. N. Watson, A treatise on the theory of Bessel functions. Cambridge Mathematical Library, 1944.

N. Wiener, The ergodic theorem, Duke Mathematical Journal, vol.5, issue.1, pp.1-18, 1939.
DOI : 10.1215/S0012-7094-39-00501-6

Y. Xu, Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres, Journal canadien de math??matiques, vol.49, issue.1, pp.175-192, 1997.
DOI : 10.4153/CJM-1997-009-4

Y. Zhi-min, A class of generalized hypergeometric functions in several variables. Canad, J. Math, vol.44, issue.6, pp.1317-1338, 1992.

H. Zeuner, One-dimensional hypergroups, Advances in Mathematics, vol.76, issue.1, pp.1-18, 1989.
DOI : 10.1016/0001-8708(89)90041-8

A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, 1959.