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Consider the Hermite operator H=−Δ+|x|2 on the Euclidean space Rn. 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.
- Hermite operator
- Higher order Riesz transforms
- Besov space
- Triebel–Lizorkin space