Hardy–Sobolev spaces associated with Hermite expansions and interpolation. (July 2017)

• Record Type: Journal Article
• Authors: Huang, Jizheng
• Is Part Of: Nonlinear analysis. Volume 157(2017)
• Page Start: 104
• Page End: 122
• Publication Date: 2017-07
• Subjects: 42C10 -- 42B25; Hermite expansions -- Hardy space -- Riesz transform -- Sobolev space; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.03.014
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let A = − Δ + | x | 2 be a Hermite operator, where Δ is the Laplacian on R d . In this paper, we first define the Hardy–Sobolev spaces associated with Hermite expansions, then we give the atomic decomposition and the real interpolation with Sobolev spaces. As an application, we consider the endpoint version of the div–curl theorem for the Hermite operator.