Geodesic
Mathematical Analysis/Harmonic Analysis
Littlewood–Paley and Lusin functions on stratified groups
[Les fonctions de Littlewood–Paley et Lusin sur les groupes stratifiés]

Présenté par : Jean-Pierre Kahane

Zhao, Jiman1
1 School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China
Comptes Rendus. Mathématique, Tome 345 (2007) no. 7, pp. 377-380.

Voir la notice de l'article provenant de la source Numdam

In this Note, we define the Littlewood–Paley and Lusin functions associated with the sub-Laplacian operator on stratified groups. The Lp (1<p<∞) boundedness of Littlewood–Paley and Lusin functions are proved.

Dans cette Note, nous définissons les fonctions de Littlewood–Paley et de Lusin sur les groupes stratifiés. Nous prouvons que pour 1<p<∞, elles sont bornées sur Lp.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.09.007

Zhao, Jiman 1

1 School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China 
@article{CRMATH_2007__345_7_377_0,
     author = {Zhao, Jiman},
     title = {Littlewood{\textendash}Paley and {Lusin} functions on stratified groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {377--380},
     publisher = {Elsevier},
     volume = {345},
     number = {7},
     year = {2007},
     doi = {10.1016/j.crma.2007.09.007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2007.09.007/}
}
TY  - JOUR
AU  - Zhao, Jiman
TI  - Littlewood–Paley and Lusin functions on stratified groups
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 377
EP  - 380
VL  - 345
IS  - 7
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2007.09.007/
DO  - 10.1016/j.crma.2007.09.007
LA  - en
ID  - CRMATH_2007__345_7_377_0
ER  - 
%0 Journal Article
%A Zhao, Jiman
%T Littlewood–Paley and Lusin functions on stratified groups
%J Comptes Rendus. Mathématique
%D 2007
%P 377-380
%V 345
%N 7
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2007.09.007/
%R 10.1016/j.crma.2007.09.007
%G en
%F CRMATH_2007__345_7_377_0
Zhao, Jiman. Littlewood–Paley and Lusin functions on stratified groups. Comptes Rendus. Mathématique, Tome 345 (2007) no. 7, pp. 377-380. doi : 10.1016/j.crma.2007.09.007. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2007.09.007/

[1] J.C. Chen, Heat kernels on positively curved manifolds and applications, Ph.D. thesis, Hangzhou Univ., 1987

[2] Coulhon, T.; Duong, X.T.; Li, X.D. Littlewood−Paley−Stein functions on complete Riemannian manifolds for 1⩽p⩽2, Studia Math., Volume 154 (2003) no. 1, pp. 37-57

[3] Folland, G.B. Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Math., Volume 13 (1975) no. 2, pp. 161-207

[4] Folland, G.B. Lipschitz classes and Poisson integrals on stratified groups, Studia Math., Volume 66 (1979) no. 1, pp. 37-55

[5] Han, Y.S.; Sawyer, E.T. Littlewood–Paley theory on spaces of homogeneous type and the classical function spaces, Mem. Amer. Math. Soc., Volume 110 (1994) no. 530

[6] Lohoué, N. Estimation des fonctions de Littlewood–Paley–Stein sur les variétés riemanniennes à courbure non positive, Ann. Sci. École Norm. Sup. (4), Volume 20 (1987), pp. 505-544 (in French)

[7] Lohoué, N. Transformées de Riesz et fonctions de Littlewood–Paley sur les groupes non moyennables, C. R. Acad. Sci. Paris Sér. I Math., Volume 306 (1988) no. 7, pp. 327-330 (in French)

[8] Meda, S. On the Littlewood–Paley–Stein g-function, Trans. Amer. Math. Soc., Volume 347 (1995) no. 6, pp. 2201-2212

[9] Stein, E.M. Topics in Harmonic Analysis Related to the Littlewood–Paley Theory, Annals of Mathematics Studies, vol. 63, Princeton Univ. Press, Univ. of Tokyo Press, 1970

[10] Stein, E.M. Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, vol. 30, Princeton Univ. Press, 1970

[11] Stein, E.M. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, 1993

Cité par Sources :