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: Harboure, E., De Rosa, L., Segovia, C., Torrea, J.L.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00255831_v328_n4_p653_Harboure
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00255831_v328_n4_p653_Harboure2023-10-03T14:36:17Z Lp-dimension free boundedness for Riesz transforms associated to Hermite functions Harboure, E. De Rosa, L. Segovia, C. Torrea, J.L. 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. Fil:Harboure, E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:De Rosa, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00255831_v328_n4_p653_Harboure
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description 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.
format JOUR
author Harboure, E.
De Rosa, L.
Segovia, C.
Torrea, J.L.
spellingShingle Harboure, E.
De Rosa, L.
Segovia, C.
Torrea, J.L.
Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
author_facet Harboure, E.
De Rosa, L.
Segovia, C.
Torrea, J.L.
author_sort Harboure, E.
title Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
title_short Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
title_full Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
title_fullStr Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
title_full_unstemmed Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
title_sort lp-dimension free boundedness for riesz transforms associated to hermite functions
url http://hdl.handle.net/20.500.12110/paper_00255831_v328_n4_p653_Harboure
work_keys_str_mv AT harbouree lpdimensionfreeboundednessforriesztransformsassociatedtohermitefunctions
AT derosal lpdimensionfreeboundednessforriesztransformsassociatedtohermitefunctions
AT segoviac lpdimensionfreeboundednessforriesztransformsassociatedtohermitefunctions
AT torreajl lpdimensionfreeboundednessforriesztransformsassociatedtohermitefunctions
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