Boundedness criterion of Journé’s class of singular integrals on multiparameter Hardy spaces

This article concerns nonconvolutional type operators (also known as Journé’s type operators) associated with a multiparameter family of dilations given by (x1, x2, . . . , xm)→(δ1x1, δ2x2, . . . , δmxm) where x1 ∈ Rn1, x2 ∈ Rn2, . . . , xm ∈ Rnm and m 3. We are especially interested in the boundedness of such operators on the multiparameter Hardy spaces. This work is motivated by Pipher’s result on the boundedness of these operators from the multiparameter Hp spaces to Lp spaces for 0