Abstract
Consider the Hermite operator (Formula presented.) on the Euclidean space (Formula presented.). The main aim of this article is to develop a theory of homogeneous and inhomogeneous Besov and Triebel–Lizorkin spaces associated to the Hermite operator. Our inhomogeneous Besov and Triebel–Lizorkin spaces are different from those introduced by Petrushev and Xu (J Fourier Anal Appl 14, 372–414 2008). As applications, we show the boundedness of negative powers and spectral multipliers of the Hermite operators on some appropriate Besov and Triebel–Lizorkin spaces.
Original language | English |
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Pages (from-to) | 405-448 |
Number of pages | 44 |
Journal | Journal of Fourier Analysis and Applications |
Volume | 21 |
Issue number | 2 |
DOIs | |
Publication status | Published - Apr 2015 |
Keywords
- Besov space
- Hermite operator
- Molecular decomposition
- Triebel–Lizorkin space