Generalized Besov type spaces on the Laguerre hypergroup
Annales mathématiques Blaise Pascal, Volume 12 (2005) no. 1, pp. 117-145.

In this paper we study generalized Besov type spaces on the Laguerre hypergroup and we give some characterizations using different equivalent norms which allows to reach results of completeness, continuous embeddings and density of some subspaces. A generalized Calderón-Zygmund formula adapted to the harmonic analysis on the Laguerre Hypergroup is obtained inducing two more equivalent norms.

DOI: 10.5802/ambp.198
Assal, Miloud 1; Ben Abdallah, Hacen 2

1 IPEIN. Campus Universitaire Département de Mathématiques Mrezka 8000 Nabeul Tunisia
2 Faculté des Sciences de Bizerte Département de Mathématiques Zarzouna 7021 Bizerte Tunisia
@article{AMBP_2005__12_1_117_0,
     author = {Assal, Miloud and Ben Abdallah, Hacen},
     title = {Generalized {Besov} type spaces on the {Laguerre} hypergroup},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {117--145},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {12},
     number = {1},
     year = {2005},
     doi = {10.5802/ambp.198},
     zbl = {1098.42016},
     mrnumber = {2126444},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/ambp.198/}
}
TY  - JOUR
AU  - Assal, Miloud
AU  - Ben Abdallah, Hacen
TI  - Generalized Besov type spaces on the Laguerre hypergroup
JO  - Annales mathématiques Blaise Pascal
PY  - 2005
SP  - 117
EP  - 145
VL  - 12
IS  - 1
PB  - Annales mathématiques Blaise Pascal
UR  - http://www.numdam.org/articles/10.5802/ambp.198/
DO  - 10.5802/ambp.198
LA  - en
ID  - AMBP_2005__12_1_117_0
ER  - 
%0 Journal Article
%A Assal, Miloud
%A Ben Abdallah, Hacen
%T Generalized Besov type spaces on the Laguerre hypergroup
%J Annales mathématiques Blaise Pascal
%D 2005
%P 117-145
%V 12
%N 1
%I Annales mathématiques Blaise Pascal
%U http://www.numdam.org/articles/10.5802/ambp.198/
%R 10.5802/ambp.198
%G en
%F AMBP_2005__12_1_117_0
Assal, Miloud; Ben Abdallah, Hacen. Generalized Besov type spaces on the Laguerre hypergroup. Annales mathématiques Blaise Pascal, Volume 12 (2005) no. 1, pp. 117-145. doi : 10.5802/ambp.198. http://www.numdam.org/articles/10.5802/ambp.198/

[1] Assal, M.; Nessibi, M. M. Sobolev Type Spaces on the Dual of the Laguerre Hypergroup, Potential Analysis, Volume 20 (2004), pp. 85-103 | DOI | MR | Zbl

[2] Bahouri, H.; Gérard, P.; Xu, C. J. Espaces de Besov et Estimations de Strichartz Généralisées sur le Groupe de Heisenberg, Journal d’Analyse Mathématique, Volume 82 (2000) | Zbl

[3] Besov, O. V. On a Family of Function Spaces in Connection with Embeddings and Extensions, Trudy Mat. Inst. Steklov, Volume 60 (1961), pp. 42-81 | MR | Zbl

[4] Betancor, J. J.; Rodríguez-Mesa, L. On the Besov-Hankel Spaces, Math. Soc. Japan, Volume 50 n ∘ 3 (1998), pp. 781-788 | DOI | MR | Zbl

[5] Bloom, W. R.; Heyer, H. Harmonic Analysis of Probability Measures on Hypergroups, de Gruyter studies in Mathematics 20, de Gruyter, Berlin / New York, 1994 | MR | Zbl

[6] Bourdaud, G. Réalisation des Espaces de Besov Homogènes, Arkiv for Mat., Volume 26 (1988), pp. 41-54 | DOI | MR | Zbl

[7] Bourdaud, G. Analyse Fonctionnelle dans l’Espace Euclidien, Publications Mathématiques de Paris 7, 1995 | Zbl

[8] Chemin, J.-Y About Navier-Stokes System, Publication du Laboratoire d’Analyse Numerique, Université Pierre et Marie Curie, 1996

[9] Coulhon, T.; Russ, E.; Tardivel-Nachef, V. Sobolev Algebras on Lie Groups and Riemannian Manifolds, Amer. J. of Math., Volume 123 (2001), pp. 283-342 | DOI | MR | Zbl

[10] Delsarte, J. Sur une Extension de la Formule de Taylor, J. Math. et Appl., Volume 17, Fasc. III (1938), pp. 213-231

[11] Erdélyi, A.; Magnus, W.; Aberthettinger, F.; Tricomi, G. Higher Transcendental Functions. Vol II, M.G Graw-Hill, New York, 1993 | Zbl

[12] Faraut, J.; Harzallah, K. Deux cours d’Analyse Harmonique, Ecole d’été d’Analyse Harmonique de Tunis, Birkhäuser, 1984 | Zbl

[13] Fitouhi, A.; Hamza, M. M. Expansion In Series of Laguerre Functions for Solution of Perturbed Laguerre Equations (to appear in Contemporary Mathematics of A.M.S.) | Zbl

[14] Frazier, M.; Jawerth, B.; Weiss, G. Sur une Extension de la Formule de Taylor, C.B.M.S, Amer. Math. Soc., Providence, Rhod Island, Volume 79 (1991) | MR

[15] Jewett, R. I. Spaces with an Abstract Convolution of Measures, Adv. in Math., Volume 18 (1975), pp. 1-101 | DOI | MR | Zbl

[16] Koornwinder, T. H. Positivity Proofs for Linearisation and Connection Coefficients of Orthogonal Polynomials Satisfying an Addition Formula, J. London. Math. Soc., Volume 18 (1978), pp. 101-1114 | DOI | MR | Zbl

[17] Lebedev, N. M. Special Function and Their Applications, Dover, New York, 1972 | MR | Zbl

[18] Nessibi, M. M.; Sifi, M. Laguerre Hypergroup and Limit Theorem, B.P. Komrakov, I.S. Krasil’shchik, G.L. Litvinov and A.B. Sossinsky (eds.), Lie Groups and Lie Algebra-Their Representations, Generalizations and Applications, Kluwer Acad. Publ. Dordrecht (1998), pp. 133-145 | Zbl

[19] Nessibi, M. M.; Trimèche, K. Inversion of the Radon Transform on the Laguerre Hypergroup by Using Generalized Wavelets, Journal of mathematical analysis and application, Volume 208 (1997), pp. 337-363 | DOI | MR | Zbl

[20] Peetre, J. New Thoughts on Besov Spaces, Duke Univ. Math. Serie Durham, Univ. (1976) | MR | Zbl

[21] Stein, E. M. Harmonic Analysis: Real Variable Methods, Orthogonality and Ossillatory Integrals, Princeton University Press, 1993 | MR | Zbl

[22] Stempak, K. An Algebra Associated With the Generalized Sublaplacian, Studia Math., Volume 88 (1988), pp. 245-256 | MR | Zbl

[23] Stempak, K. Mean of Summability Methods for Laguerre Series, Transactions of the American mathematical society, Volume 322, Number 2 (December 1990) | MR | Zbl

[24] Triebel, H. Theory of Function Spaces, Birkhäuser, 1983 | MR

Cited by Sources: