Higher-Order Riesz Transforms of Hermite Operators on New Besov and Triebel–Lizorkin Spaces

Abstract

Consider the Hermite operator $$H=-\Delta +|x|^2$$ on the Euclidean space $${\mathbb {R}}^n$$. The aim of this article is to prove the boundedness of higher-order Riesz trnsforms on appropriate Besov and Triebel–Lizorkin spaces. As an application, we prove certain regularity estimates of second-order elliptic equations in divergence form with the oscillator perturbations.