TY - JOUR
T1 - Commutators of Riesz transforms of magnetic Schrödinger operators
AU - Duong, Xuan Thinh
AU - Yan, Lixin
PY - 2008/10
Y1 - 2008/10
N2 - Let A = -(∇ - ia→)·(∇ - ia →) + V be a magnetic Schrödinger operator acting on L 2(ℝn), n ≥ 1, where a→ = (a 1,...,an) ∈ Lloc
2 (ℝn, ℝn) and 0 ≤ V ∈ L loc
1(ℝn). In this paper, we show that when a function b ∈ BMO(ℝn), the commutators [b, T k]f = Tk(bf) - bTk f, k = 1,..., n, are bounded on Lp(ℝn) for all 1 < p < 2, where the operators Tk are Riesz transforms (∂/∂xk - iak)A-1/2 associated with A.
AB - Let A = -(∇ - ia→)·(∇ - ia →) + V be a magnetic Schrödinger operator acting on L 2(ℝn), n ≥ 1, where a→ = (a 1,...,an) ∈ Lloc
2 (ℝn, ℝn) and 0 ≤ V ∈ L loc
1(ℝn). In this paper, we show that when a function b ∈ BMO(ℝn), the commutators [b, T k]f = Tk(bf) - bTk f, k = 1,..., n, are bounded on Lp(ℝn) for all 1 < p < 2, where the operators Tk are Riesz transforms (∂/∂xk - iak)A-1/2 associated with A.
UR - http://www.scopus.com/inward/record.url?scp=52549094498&partnerID=8YFLogxK
U2 - 10.1007/s00229-008-0202-y
DO - 10.1007/s00229-008-0202-y
M3 - Article
AN - SCOPUS:52549094498
SN - 0025-2611
VL - 127
SP - 219
EP - 234
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
IS - 2
ER -