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

Abstract

The purpose of this article is to establish the molecular decomposition of the homogeneous Besov-Morrey spaces associated with the Hermite operator H = −∆ + |x| 2 on the Euclidean space Rn. Particularly, we obtain some estimates for the operator H on the Hermite-Besov-Morrey spaces and the regularity results to the fractional Hermite equations (−∆ + |x| 2 ) su = f, and (−∆ + |x| 2 + I) su = f. Our results generalize some results by Anh and Thinh [1]