Bellman functions and dimension free Lp-estimates for the Riesz transforms in Bessel settings. (August 2020)

• Record Type: Journal Article
• Authors: Betancor, Jorge J.; Dalmasso, Estefanía; Fariña, Juan C.; Scotto, Roberto
• Is Part Of: Nonlinear analysis. Volume 197(2020)
• Publication Date: 2020-08
• Subjects: 42A50 -- 42B20 -- 42B25; Riesz transforms -- Bessel operators -- Bellman functions -- Dimension free -- Bilinear embeddings; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111850
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this article we prove dimension free L p –boundedness of Riesz transforms associated with a Bessel differential operator. We obtain explicit estimates of the L p –norms for the Bessel–Riesz transforms in terms of p, establishing a linear behavior with respect to p . We use the Bellman function technique to prove a bilinear dimension free inequality involving Poisson semigroups defined through this Bessel operator.