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

Abstract EN

The authors prove that Marcinkiewicz integral operator is not only are bounded on L p , for 1 < P < ∞ , but also a bounded map from L 1 ( R n ) to weak L 1 ( R n ) .

Meanwhile, the B M O L -boundedness and ( H L 1 , L 1 ) -boundedness are also obtained.

Finally, the L p -boundedness and ( L ∞ , B M O L ) -boundedness for the commutator of Marcinkiewicz integral of schrödinger type are established.