Geodesic
Mixed norm estimates for the Riesz transforms associated to Dunkl harmonic oscillators
Pradeep, Boggarapu1 ; Thangavelu, Sundaram1 
1 Department of Mathematics Indian Institute of Science Bangalore-560012 (India)
Annales mathématiques Blaise Pascal, Tome 22 (2015) no. 1, pp. 89-120

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

In this paper we study weighted mixed norm estimates for Riesz transforms associated to Dunkl harmonic oscillators. The idea is to show that the required inequalities are equivalent to certain vector valued inequalities for operator defined in terms of Laguerre expansions. In certain cases the main result can be deduced from the corresponding result for Hermite Riesz transforms.

DOI : 10.5802/ambp.347
Classification : 42C10, 47G40, 26A33, 43A90, 42B20, 42B35, 33C44
Keywords: Reflection groups, Dunkl operators, Hermite and generalised Hermite functions, Riesz transforms, singular integrals, weighted inequalities.

Pradeep, Boggarapu 1 ; Thangavelu, Sundaram 1

1 Department of Mathematics Indian Institute of Science Bangalore-560012 (India) 
@article{AMBP_2015__22_1_89_0,
     author = {Pradeep, Boggarapu and Thangavelu, Sundaram},
     title = {Mixed norm estimates for the {Riesz} transforms associated to {Dunkl} harmonic oscillators},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {89--120},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {22},
     number = {1},
     year = {2015},
     doi = {10.5802/ambp.347},
     zbl = {1327.42031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/ambp.347/}
}
TY  - JOUR
AU  - Pradeep, Boggarapu
AU  - Thangavelu, Sundaram
TI  - Mixed norm estimates for the Riesz transforms associated to Dunkl harmonic oscillators
JO  - Annales mathématiques Blaise Pascal
PY  - 2015
SP  - 89
EP  - 120
VL  - 22
IS  - 1
PB  - Annales mathématiques Blaise Pascal
UR  - http://geodesic.mathdoc.fr/articles/10.5802/ambp.347/
DO  - 10.5802/ambp.347
LA  - en
ID  - AMBP_2015__22_1_89_0
ER  - 
%0 Journal Article
%A Pradeep, Boggarapu
%A Thangavelu, Sundaram
%T Mixed norm estimates for the Riesz transforms associated to Dunkl harmonic oscillators
%J Annales mathématiques Blaise Pascal
%D 2015
%P 89-120
%V 22
%N 1
%I Annales mathématiques Blaise Pascal
%U http://geodesic.mathdoc.fr/articles/10.5802/ambp.347/
%R 10.5802/ambp.347
%G en
%F AMBP_2015__22_1_89_0
Pradeep, Boggarapu; Thangavelu, Sundaram. Mixed norm estimates for the Riesz transforms associated to Dunkl harmonic oscillators. Annales mathématiques Blaise Pascal, Tome 22 (2015) no. 1, pp. 89-120. doi: 10.5802/ambp.347

Cité par Sources :