Commutators of Singular Integral Operators Related to Magnetic Schrdinger Operators

摘要

Let A:=-(▽-ia(向量))·(?-ia(向量))+V be a magnetic Schrdinger operator on L^2(R^n),n≥2,where a(向量)=(a_1,···,a_n)∈L^2_(loc)(R^n,R^n) and 0≤V∈L^1_(loc)(R^n).In this paper,we show that for a function b in Lipschitz space Lip_α(R^n) with α∈(0,1),the commutator[b,V^(1/2)A^(-1/2)] is bounded from L_p(R^n) to L_q(R^n),where p,q∈(1,2] and 1/p-1/q =α/n.