The Boundedness of Marcinkiewicz Integral Associated with Schrödinger Operator and Its Commutator

Abstract

The authors prove that Marcinkiewicz integral operator is not only are bounded on Lp, for 1<P<∞, but also a bounded map from L1(Rn) to weak L1(Rn). Meanwhile, the BMOL-boundedness and (HL1,L1)-boundedness are also obtained. Finally, the Lp-boundedness and (L∞,BMOL)-boundedness for the commutator of Marcinkiewicz integral of schrödinger type are established.