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).

中文翻译：

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与Hermite算子相关的Triebel–Lizorkin–Morrey空间

本文的目的是在欧氏空间\上建立与Hermite算子\（\ mathbb {H} \ equiv-\ Delta + | x | ^ 2 \）相关的同构和非同构Triebel-Lizorkin-Morrey空间的分子分解。（\ mathbb {R} ^ n \）。作为分子分解理论的应用，我们证明了与算子\（{\ mathbb {H}} \）相关的Riesz势，Bessel势和谱乘法器的Triebel–Lizorkin–Morrey有界性。这些结果概括了Bui和Duong中的相应结果（J Fourier Anal Appl 21：405–448，2015）。