Hardy spaces and Campanato spaces associated with Laguerre expansions and higher order Riesz transforms

Let ${\mathcal{L}}_{\nu }$ be the Laguerre differential operator which is the self-adjoint extension of the differential operator $$L_{\nu }:=\sum _{i=1}^n[-\frac{{\mathrm{\partial }}^2}{\mathrm{\partial }{x}_i^2}+x_i^2+\frac{1}{x_i^2}({\nu }_i^2-\frac{1}{4})]$$ initially defined on $C_c^{\mathrm{\infty }}({\mathbb{R}}_{+}^n)$ as its natural domain, where $\nu \in [-1\mathrm{/}2,\mathrm{\infty }{)}^n$, $n\ge 1$. In this paper, we first develop the theory of Hardy spaces $H_{{\mathcal{L}}_{\nu }}^p$ associated with ${\mathcal{L}}_{\nu }$ for the full range $p\in (0,1]$. Then we investigate the corresponding BMO-type spaces and establish that they coincide with the dual spaces of $H_{{\mathcal{L}}_{\nu }}^p$. Finally, we show boundedness of higher-order Riesz transforms on Lebesgue spaces, as well as on our new Hardy and BMO-type spaces.