The Boundedness Of Multi-parameter Littlewood-Paley Operators On Hardy Spaces

Suppose that n,m≥1 and λ=(λ1,λ2)with λ1,λ2>1.For any x=(x1,x2)∈Rn×Rm,then multi-parameter Littlewood-Paley gλ*functions gλ*(f)defined by gλ(f)(x1,x2)where Kt1,t2(f)(y1,y2)=∫∫Rn×Rm(y1,y2,z1,z2)f(z1,z2)dz1dz2.In this dis-sertation,applying the atomic decomposition of product Hardy spaces and Journe covering Lemma,we verify that multi-parameter Littlewood-Paley gλ*functions are bounded from Hp(Rn×Rm)to Lp(Rn×Rm)with max{n/n+α,m/m+β}<p≤1.