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.
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Acknowledgements
Xuan Thinh Duong was supported by the Australian Research Council through the Grant ARC DP190100970. The authors would like to thank the referees for their useful comments and suggestions to improve the paper.
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Communicated by Peneho Petrushev.
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Bui, T.A., Duong, X.T. Higher-Order Riesz Transforms of Hermite Operators on New Besov and Triebel–Lizorkin Spaces. Constr Approx 53, 85–120 (2021). https://doi.org/10.1007/s00365-019-09493-y
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DOI: https://doi.org/10.1007/s00365-019-09493-y