Triebel–Lizorkin–Morrey spaces associated to Hermite operators

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 R n . As applications of the molecular decomposition theory, we show the Triebel–Lizorkin–Morrey...

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Bibliographic Details
Published in:Revista matemática complutense 2020-05, Vol.33 (2), p.527-555
Main Authors: Trong, Nguyen Ngoc, Truong, Le Xuan, Dung, Tran Tri, Vo, Hanh Nguyen
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Decomposition
Euclidean geometry
Euclidean space
Geometry
Mathematics
Mathematics and Statistics
Topology
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Summary: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 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 H . These results generalize the corresponding results in Bui and Duong (J Fourier Anal Appl 21:405–448, 2015 ).
ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-019-00314-1