Electron. J. Differential Equations, Vol. 2018 (2018), No. 187, pp. 1-14.

Besov-Morrey spaces associated with Hermite operators and applications to fractional Hermite equations

Nguyen Anh Dao, Nguyen Ngoc Trong, Le Xuan Truong

Abstract:
The purpose of this article is to establish the molecular decomposition of the homogeneous Besov-Morrey spaces associated with the Hermite operator $\mathbb{H} = -\Delta+|x|^2$ on the Euclidean space $\mathbb{R}^n$. Particularly, we obtain some estimates for the operator $\mathbb{H}$ on the Hermite-Besov-Morrey spaces and the regularity results to the fractional Hermite equations
$$ (-\Delta +|x|^2 )^su=f, $$
and
$$ (-\Delta +|x|^2 +I)^su=f. $$
Our results generalize some results by Anh and Thinh [1].

Submitted September 26, 2018. Published November 20, 2018.
Math Subject Classifications: 42B35, 42B20.
Key Words: Fractional Hermite equations; Hermite-Besov-Morrey space; molecular decomposition.

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  Nguyen Anh Dao
Applied Analysis Research Group
Faculty of Mathematics and Statistics
Ton Duc Thang University
HoChiMinh City, Vietnam
email: daonguyenanh@tdtu.edu.vn
  Nguyen Ngoc Trong
Faculty of Mathematics and Computer Science
VUNHCM - University of Science
HoChiMinh city, Vietnam email: trongnn37@gmail.com
Le Xuan Truong
Department of Mathematics and Statistics
University of Economics
HoChiMinh City, Vietnam
email: lxuantruong@gmail.com

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