Abstract
For a root system R on
Acknowledgements
The authors would like to thank the referee for valuable comments and suggestions which improved the presentation of the paper.
References
[1] D. R. Adams and L. I. Hedberg, Function Spaces and Potential Theory, Grundlehren Math. Wiss. 314, Springer, Berlin, 1996. 10.1007/978-3-662-03282-4Suche in Google Scholar
[2] D. H. Armitage and S. J. Gardiner, Classical Potential Theory, Springer Monogr. Math., Springer, London, 2001. 10.1007/978-1-4471-0233-5Suche in Google Scholar
[3] F. Dai and H. Wang, A transference theorem for the Dunkl transform and its applications, J. Funct. Anal. 258 (2010), no. 12, 4052–4074. 10.1016/j.jfa.2010.03.006Suche in Google Scholar
[4] M. F. E. de Jeu, The Dunkl transform, Invent. Math. 113 (1993), no. 1, 147–162. 10.1007/BF01244305Suche in Google Scholar
[5] L. Deleaval, Two results on the Dunkl maximal operator, Studia Math. 203 (2011), no. 1, 47–68. 10.4064/sm203-1-3Suche in Google Scholar
[6] C. F. Dunkl, Integral kernels with reflection group invariance, Canad. J. Math. 43 (1991), no. 6, 1213–1227. 10.4153/CJM-1991-069-8Suche in Google Scholar
[7] C. F. Dunkl, Hankel transforms associated to finite reflection groups, Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications (Tampa 1991), Contemp. Math. 138, American Mathematical Society, Providence (1992), 123–138. 10.1090/conm/138/1199124Suche in Google Scholar
[8] C. F. Dunkl and Y. Xu, Orthogonal Polynomials of Several Variables, Encyclopedia Math. Appl. 81, Cambridge University Press, Cambridge, 2001. 10.1017/CBO9780511565717Suche in Google Scholar
[9] L. Gallardo and C. Rejeb, A new mean value property for harmonic functions relative to the Dunkl–Laplacian operator and applications, Trans. Amer. Math. Soc. 368 (2016), no. 5, 3727–3753. 10.1090/tran/6671Suche in Google Scholar
[10] L. Gallardo and C. Rejeb, Support properties of the intertwining and the mean value operators in Dunkl theory, preprint (2016), https://hal.inria.fr/hal-01331693/document. 10.1090/proc/13478Suche in Google Scholar
[11] L. Gallardo and C. Rejeb, Newtonian Potentials and subharmonic functions associated to root systems, Potential Anal. (2017), 10.1007/s11118-017-9619-9. 10.1007/s11118-017-9619-9Suche in Google Scholar
[12] S. Hassani, S. Mustapha and M. Sifi, Riesz potentials and fractional maximal function for the Dunkl transform, J. Lie Theory 19 (2009), no. 4, 725–734. Suche in Google Scholar
[13] W. K. Hayman and P. B. Kennedy, Subharmonic Functions. Vol. I, London Math. Soc. Monogr. Ser. 9, Academic Press, London, 1976. Suche in Google Scholar
[14] L. I. Hedberg, On certain convolution inequalities, Proc. Amer. Math. Soc. 36 (1972), 505–510. 10.1090/S0002-9939-1972-0312232-4Suche in Google Scholar
[15] L. L. Helms, Potential Theory, Universitext, Springer, London, 2009. 10.1007/978-1-84882-319-8Suche in Google Scholar
[16] J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Stud. Adv. Math. 29, Cambridge University Press, Cambridge, 1990. 10.1017/CBO9780511623646Suche in Google Scholar
[17] R. Kane, Reflection Groups and Invariant Theory, CMS Books Math./Ouvrages Math. SMC 5, Springer, New York, 2001. 10.1007/978-1-4757-3542-0Suche in Google Scholar
[18] N. S. Landkof, Foundations of Modern Potential Theory, Grundlehren Math. Wiss. 180, Springer, New York, 1972. 10.1007/978-3-642-65183-0Suche in Google Scholar
[19] E. M. Opdam, Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group, Compos. Math. 85 (1993), no. 3, 333–373. Suche in Google Scholar
[20] C. Rejeb, Volume mean operator and differentiation results associated to root systems, Bull. Korean Math. Soc. (2017), 10.4134/BKMS.b160675. 10.4134/BKMS.b160675Suche in Google Scholar
[21] M. Rösler, Generalized Hermite polynomials and the heat equation for Dunkl operators, Comm. Math. Phys. 192 (1998), no. 3, 519–542. 10.1007/s002200050307Suche in Google Scholar
[22] M. Rösler, Positivity of Dunkl’s intertwining operator, Duke Math. J. 98 (1999), no. 3, 445–463. 10.1215/S0012-7094-99-09813-7Suche in Google Scholar
[23] M. Rösler, A positive radial product formula for the Dunkl kernel, Trans. Amer. Math. Soc. 355 (2003), no. 6, 2413–2438. 10.1090/S0002-9947-03-03235-5Suche in Google Scholar
[24] M. Rösler, Dunkl operators: Theory and applications, Orthogonal Polynomials and Special Functions (Leuven 2002), Lecture Notes in Math. 1817, Springer, Berlin (2003), 93–135. 10.1007/3-540-44945-0_3Suche in Google Scholar
[25] M. Rösler and M. de Jeu, Asymptotic analysis for the Dunkl kernel, J. Approx. Theory 119 (2002), no. 1, 110–126. 10.1006/jath.2002.3722Suche in Google Scholar
[26] M. Rösler and M. Voit, Markov processes related with Dunkl operators, Adv. Appl. Math. 21 (1998), no. 4, 575–643. 10.1006/aama.1998.0609Suche in Google Scholar
[27] L. Schwartz, Théorie des distributions. Nouvelle édition, entièrement corrigée, refondue et augmentée, Hermann, Paris, 1966. Suche in Google Scholar
[28] S. Thangavelu and Y. Xu, Convolution operator and maximal function for the Dunkl transform, J. Anal. Math. 97 (2005), 25–55. 10.1007/BF02807401Suche in Google Scholar
[29] S. Thangavelu and Y. Xu, Riesz transform and Riesz potentials for Dunkl transform, J. Comput. Appl. Math. 199 (2007), no. 1, 181–195. 10.1016/j.cam.2005.02.022Suche in Google Scholar
[30] K. Trimèche, The Dunkl intertwining operator on spaces of functions and distributions and integral representation of its dual, Integral Transforms Spec. Funct. 12 (2001), no. 4, 394–374. 10.1080/10652460108819358Suche in Google Scholar
[31] K. Trimèche, Paley–Wiener theorems for the Dunkl transform and Dunkl translation operators, Integral Transforms Spec. Funct. 13 (2002), no. 1, 17–38. 10.1080/10652460212888Suche in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Transitivities of maps on G-spaces
- Lp-L2 estimates for solutions of the wave equation associated to the Grushin operator
- Gabor orthonormal bases generated by indicator functions of parallelepiped-shaped sets
- Riesz potentials of Radon measures associated to reflection groups
- Harmonic vector fields on a weighted Riemannian manifold arising from a Finsler structure
- An efficient method to compute the Moore–Penrose inverse
- The Thirring model in spaces of analytic functions
Artikel in diesem Heft
- Frontmatter
- Transitivities of maps on G-spaces
- Lp-L2 estimates for solutions of the wave equation associated to the Grushin operator
- Gabor orthonormal bases generated by indicator functions of parallelepiped-shaped sets
- Riesz potentials of Radon measures associated to reflection groups
- Harmonic vector fields on a weighted Riemannian manifold arising from a Finsler structure
- An efficient method to compute the Moore–Penrose inverse
- The Thirring model in spaces of analytic functions