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Let H=−Δ+|x|2 be the harmonic oscillator on Rn. In this paper, we prove estimates on Besov spaces associated to the operator H and the end-point maximal regularity estimates for the fractional harmonic oscillator Hα, 0<α≤1, on the Besov spaces associated to the harmonic oscillator H. These spaces are the appropriate function spaces for the study of estimates on Besov type spaces and the end-point maximal regularity estimates for the fractional power Hα in the sense that similar estimates might fail with the classical Besov spaces.
|Number of pages||36|
|Journal||Journal of Differential Equations|
|Publication status||Published - 5 Apr 2021|
- Harmonic oscillator
- Heat kernel
- Maximal regularity
- Besov space
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Harmonic analysis and dispersive partial differential equations
Li, J., Guo, Z., Kenig, C. & Nakanishi, K.
31/01/17 → …
Harmonic analysis: function spaces and partial differential equations
Duong, X., Hofmann, S., Ouhabaz, E. M. & Wick, B.
11/02/19 → 10/02/22