Compact commutators of Riesz transforms associated to Schrödinger operator (Q713620)

The authors study the compactness of some commutators of Riesz transforms associated to the Schrödinger operator \(L=-\Delta+V\) on \(\mathbb R^n\) with \(n\geq3\), where the potential \(V\) is nonzero, nonnegative and belongs to the reverse Hölder class \(B_q\) for \(q>n/2\). It is proved that, if \(T_1=(-\Delta+V)^{-1}V\), \(T_2=(-\Delta+V)^{-1/2}V^{-1/2}\) and \(T_3=(-\Delta+V)^{-1/2}\nabla\), then the commutators \([b,Tj]\), \(j=1,2,3\), are compact on \(L^p(\mathbb R^n)\) when \(p\) ranges in an interval and \(b\in VMO(\mathbb R^n)\).