Boundedness of inhomogeneous Journé's type operators on multi-parameter local Hardy spaces. (August 2020)

• Record Type: Journal Article
• Authors: Ding, Wei; Lu, Guozhen
• Is Part Of: Nonlinear analysis. Volume 197(2020)
• Publication Date: 2020-08
• Subjects: 42B35 -- 42B30 -- 42B25 -- 42B20; Inhomogeneous Calderón–Zygmund operators -- Multi-parameter local Hardy spaces -- Littlewood–Paley–Stein theory; 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.2020.111816
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we establish a boundedness criterion of a class of inhomogeneous Journé's type of multi-parameter singular integral operators on multi-parameter local Hardy spaces h p ( R n 1 × ⋯ × R n k ) recently introduced in Ding et al. (2019). The consideration of such inhomogeneous Journé's type of multi-parameter singular integral operators is motivated by the study of the multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces. The lack of the vanishing moments of both the corresponding functions in the multi-parameter local Calderón reproducing formula and the multi-parameter local Littlewood–Paley–Stein functions, as well as the lack of vanishing moments of atoms in the multi-parameter local Hardy spaces h p ( R n 1 × ⋯ × R n k ) with large size all create substantial difficulties in our proofs.