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.

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
Mots-clés : 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) 
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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. http://www.numdam.org/articles/10.5802/ambp.347/

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