DIMENSION FREE $L^P$ ESTIMATES FOR RIESZ TRANSFORMS ASSOCIATED WITH LAGUERRE FUNCTION EXPANSIONS OF HERMITE TYPE

Abstract

We prove dimension free $L^p$ estimates for Riesz transforms associated with multi-dimensional Laguerre function expansions of Hermite type. The range of the admissible Laguerre type multi-index $\alpha$ in these estimates depends on $p \in (1,\infty)$; for $1 \lt p \le 2$ this range is almost optimal. The proof is based on suitably defined square functions with Poisson and modified Poisson semigroups involved.