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arXiv · 1803.00789

Bellman Functions and Dimension Free $L^p$estimates for the Riesz Transforms in Bessel settings

Jorge J. Betancor·Estefanía Dalmasso·Juan C. Fariña·Roberto Scotto
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Abstract

In this article we prove dimension free $L^p$-boundedness of Riesz transforms associated with a Bessel diferential operator. We obtain explicit estimates of the $L^p$-norms for the Bessel-Riesz transforms in terms of p, establishing a linear behaviour 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.

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Jorge J. Betancor, Estefanía Dalmasso, Juan C. Fariña, Roberto Scotto. 2018-03-02. Bellman Functions and Dimension Free $L^p$estimates for the Riesz Transforms in Bessel settings. https://arxiv.org/abs/1803.00789

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