刊名:Journal of Mathematical Analysis and Applications
出版年:1 November 2014
年:2014
卷:419
期:1
页码:298-328
全文大小:463 K
文摘
We consider the Schrödinger operator L=−螖+V on Rn, where the nonnegative potential V belongs to the reverse Hölder class Bq1 for some . Let q2=1 when q1≥n and when . Set . Let be the Hardy space related to the Schrödinger operator L for . The commutator [b,R] is generated by a function , where is a function space which is larger than the classical Companato space, and the Riesz transform . We show that the commutator [b,R] is bounded from Lp(Rn) into Lq(Rn) for , where and bounded from into Lq(Rn) for , where . Moreover, we prove that the commutator [b,R] maps continuously into weak L1(Rn). At last, we give a characterization for the boundedness of the commutator [b,R] in an extreme case.