Hardy spaces, Campanato spaces and higher order Riesz transforms associated with Bessel operators

Abstract

Let $\nu =({\nu }_1,\dots ,{\nu }_n)\in (-1/2,\infty {)}^n$, with $n\ge 1$, and let ${\Delta }_{\nu }$ be the multivariate Bessel operator defined by \[ Δ_ν = -\sum_{j=1}^n\left( \frac{\partial^2}{\partial x_j^2} - \frac{ν_j^2 - 1/4}{x_j^2} \right). \] In this paper, we develop the theory of Hardy spaces and BMO-type spaces associated with the Bessel operator ${\Delta }_{\nu }$. We then study the higher-order Riesz transforms associated with ${\Delta }_{\nu }$. First, we show that these transforms are Calderón-Zygmund operators. We further prove that they are bounded on the Hardy spaces and BMO-type spaces associated with ${\Delta }_{\nu }$.

35 pages. arXiv admin note: text overlap with arXiv:2504.09867