Higher order Riesz transforms for Hermite expansions

Abstract

Abstract In this paper, we consider the Riesz transform of higher order associated with the harmonic oscillator L = − Δ + | x | 2 $L=-\Delta+|x|^{2}$ , where Δ is the Laplacian on R d $\mathbb {R}^{d}$ . Moreover, the boundedness of Riesz transforms of higher order associated with Hermite functions on the Hardy space is proved.

Keywords

• Hermite expansions
• Littlewood-Paley g-function
• Riesz transform
• Hardy space