Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
Riesz transforms associated to Hermite functions were introduced by S. Thangavelu, who proved that they are bounded operators on L p(ℝd), 1 < p < ∞. In this paper we give a different proof that allows us to show that the Lp-norms of these operators are bounded by a constant not dependi...
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| Autores principales: | , , , |
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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00255831_v328_n4_p653_Harboure |
| Aporte de: |
| Sumario: | Riesz transforms associated to Hermite functions were introduced by S. Thangavelu, who proved that they are bounded operators on L p(ℝd), 1 < p < ∞. In this paper we give a different proof that allows us to show that the Lp-norms of these operators are bounded by a constant not depending on the dimension d. Moreover, we define Riesz transforms of higher order and free dimensional estimates of the Lp -bounds of these operators are obtained. In order to prove the mentioned results we give an extension of the Littlewood-Paley theory that we believe of independent interest. |
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