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

The Anh Bui; The Quan Bui; Xuan Thinh Duong

doi:10.1016/j.jde.2021.01.013

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 journal › Article › peer-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 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 end-point 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 (from-to)	162-197
Number of pages	36
Journal	Journal of Differential Equations
Volume	279
DOIs	https://doi.org/10.1016/j.jde.2021.01.013
Publication status	Published - 5 Apr 2021

Keywords

Harmonic oscillator
Heat kernel
Maximal regularity
Besov space

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10.1016/j.jde.2021.01.013

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title = "Regularity estimates for the Cauchy problem to a parabolic equation associated to fractional harmonic oscillators",

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.",

keywords = "Harmonic oscillator, Heat kernel, Maximal regularity, Besov space",

author = "Bui, {The Anh} and Bui, {The Quan} and Duong, {Xuan Thinh}",

year = "2021",

month = apr,

day = "5",

doi = "10.1016/j.jde.2021.01.013",

language = "English",

volume = "279",

pages = "162--197",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Regularity estimates for the Cauchy problem to a parabolic equation associated to fractional harmonic oscillators

AU - Bui, The Anh

AU - Bui, The Quan

AU - Duong, Xuan Thinh

PY - 2021/4/5

Y1 - 2021/4/5

N2 - 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.

AB - 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.

KW - Harmonic oscillator

KW - Heat kernel

KW - Maximal regularity

KW - Besov space

UR - http://www.scopus.com/inward/record.url?scp=85099916952&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP170101060

UR - http://purl.org/au-research/grants/arc/DP190100970

U2 - 10.1016/j.jde.2021.01.013

DO - 10.1016/j.jde.2021.01.013

M3 - Article

AN - SCOPUS:85099916952

VL - 279

SP - 162

EP - 197

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

ER -

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

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Keywords

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Harmonic analysis and dispersive partial differential equations

Harmonic analysis: function spaces and partial differential equations

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

Abstract

Keywords

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Projects

Harmonic analysis and dispersive partial differential equations

Harmonic analysis: function spaces and partial differential equations

Cite this