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Abstract
Let H=−Δ+x^{2} be the harmonic oscillator on R^{n}. In this paper, we prove estimates on Besov spaces associated to the operator H and the endpoint maximal regularity estimates for the fractional harmonic oscillator H^{α}, 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 endpoint maximal regularity estimates for the fractional power H^{α} in the sense that similar estimates might fail with the classical Besov spaces.
Original language  English 

Pages (fromto)  162197 
Number of pages  36 
Journal  Journal of Differential Equations 
Volume  279 
DOIs  
Publication status  Published  5 Apr 2021 
Keywords
 Harmonic oscillator
 Heat kernel
 Maximal regularity
 Besov space
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Dive into the research topics of 'Regularity estimates for the Cauchy problem to a parabolic equation associated to fractional harmonic oscillators'. Together they form a unique fingerprint.Projects
 2 Active

Harmonic analysis: function spaces and partial differential equations
Duong, X., Hofmann, S., Ouhabaz, E. M. & Wick, B.
11/02/19 → 10/02/22
Project: Other

Harmonic analysis and dispersive partial differential equations
Li, J., Guo, Z., Kenig, C. & Nakanishi, K.
31/01/17 → …
Project: Research