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

Suppose that n,m?1 and ?=(?1,?2)with ?1,?2>1.For any x=(x1,x2)?Rn×Rm,then multi-parameter Littlewood-Paley g?*functions g?*(f)defined by g?(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 g?*functions are bounded from Hp(Rn×Rm)to Lp(Rn×Rm)with max{n/n+?,m/m+?}<p?1.