Abstract
The aim of this article is to establish molecular decomposition of homogeneous and inhomogeneous Triebel–Lizorkin–Morrey spaces associated to the Hermite operator \(\mathbb {H} \equiv -\Delta +|x|^2\) on the Euclidean space \(\mathbb {R}^n\). As applications of the molecular decomposition theory, we show the Triebel–Lizorkin–Morrey boundedness of Riesz potential, Bessel potential and spectral multipliers associated to the operator \({\mathbb {H}}\). These results generalize the corresponding results in Bui and Duong (J Fourier Anal Appl 21:405–448, 2015).
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Trong, N.N., Truong, L.X., Dung, T.T. et al. Triebel–Lizorkin–Morrey spaces associated to Hermite operators. Rev Mat Complut 33, 527–555 (2020). https://doi.org/10.1007/s13163-019-00314-1
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DOI: https://doi.org/10.1007/s13163-019-00314-1