Boundedness of inhomogeneous Journé's type operators on multi-parameter local Hardy spaces. (August 2020) - Ding, Wei; Lu, Guozhen
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.