Regularity estimates for the Cauchy problem to a parabolic equation associated to fractional harmonic oscillators

The Anh Bui*, The Quan Bui, Xuan Thinh Duong

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)162-197
Number of pages36
JournalJournal of Differential Equations
Volume279
DOIs
Publication statusPublished - 5 Apr 2021

Keywords

  • Harmonic oscillator
  • Heat kernel
  • Maximal regularity
  • Besov space

Fingerprint

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.

Cite this