Bellman Functions and Dimension Free L^pestimates for the Riesz\n Transforms in Bessel settings

2018/03/02 by Jorge J. Betancor, Estefanía Dalmasso, Betancor, Jorge J. +5
Mathematics · #Advanced Harmonic Analysis Research #Mathematical Approximation and Integration #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.1803.00789

Abstract

In this article we prove dimension free L^p-boundedness of Riesz transforms\nassociated with a Bessel diferential operator. We obtain explicit estimates of\nthe L^p-norms for the Bessel-Riesz transforms in terms of p, establishing a\nlinear behaviour with respect to p. We use the Bellman function technique to\nprove a bilinear dimension free inequality involving Poisson semigroups defined\nthrough this Bessel operator.\n

Citations

• Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular

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