The aim of this article is to establish molecular decomposition of homogeneous and inhomogeneous Triebel–Lizorkin–Morrey spaces associated to the Hermite operator H≡ - Δ + | x| 2 on the Euclidean space Rn. 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 H. These results generalize the corresponding results in Bui and Duong (J Fourier Anal Appl 21:405–448, 2015).
- Hermite operator
- Triebel–Lizorkin–Morrey space
- Molecular decomposition