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

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,
 (-\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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