Besov and Triebel-Lizorkin Spaces Associated to Hermite Operators

摘要

Consider the Hermite operator on the Euclidean space . The main aim of this article is to develop a theory of homogeneous and inhomogeneous Besov and Triebel-Lizorkin spaces associated to the Hermite operator. Our inhomogeneous Besov and Triebel-Lizorkin spaces are different from those introduced by Petrushev and Xu (J Fourier Anal Appl 14, 372-414 2008). As applications, we show the boundedness of negative powers and spectral multipliers of the Hermite operators on some appropriate Besov and Triebel-Lizorkin spaces.