Harmonic Analysis Operators Associated with Multidimensional Bessel Operators

Abstract

In this paper we establish that the maximal operator and the Littlewood-Paley g-function associated with the heat semigroup defined by multidimensional Bessel operators are of weak type (1,1). Also, we prove that Riesz transforms in the multidimensional Bessel setting are of strong type (p,p), for every $1<p<\infty$, and of weak type (1,1).

38 pages

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• Solutions of Weinstein equations representable by Bessel Poisson integrals of BMO functions
• Mapping properties of fundamental harmonic analysis operators in the exotic Bessel framework
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• Bellman Functions and Dimension Free $L^p$estimates for the Riesz Transforms in Bessel settings