Let A=-( -ia)·( -ia)+V be a magnetic Schrodinger operator on L^2(R^n),n〉2,where a:=(a1,…,an)∈Lloc^2(R^n,R^n) and 0≤V ∈Lloc^1(R^n).In this paper, we show that for a function b in Lipschitz space...Let A=-( -ia)·( -ia)+V be a magnetic Schrodinger operator on L^2(R^n),n〉2,where a:=(a1,…,an)∈Lloc^2(R^n,R^n) and 0≤V ∈Lloc^1(R^n).In this paper, we show that for a function b in Lipschitz space Lipa(R^n)with a∈(0,1),the commutator [b,V1/2A^-1/2]is bounded from L^p(R^n)to L^q(R^n),where p,q∈(1,2] and 1/p-1/q=a/n.展开更多
基金supported by the National Natural Science Foundation of China (No.11671031 and No.11471018)the Fundamental Research Funds for the Central Universities (No.FRF-BR-17-004B)Program for New Century Excellent Talents in University,Beijing Municipal Science and Technology Project (No.Z17111000220000)
文摘Let A=-( -ia)·( -ia)+V be a magnetic Schrodinger operator on L^2(R^n),n〉2,where a:=(a1,…,an)∈Lloc^2(R^n,R^n) and 0≤V ∈Lloc^1(R^n).In this paper, we show that for a function b in Lipschitz space Lipa(R^n)with a∈(0,1),the commutator [b,V1/2A^-1/2]is bounded from L^p(R^n)to L^q(R^n),where p,q∈(1,2] and 1/p-1/q=a/n.