Compact Commutators of Riesz Transforms Associated to Schrodinger Operator

Pengtao Li, Lizhong Peng
2012 Pure and Applied Mathematics Quarterly  
In this paper, we consider the compactness of some commutators of Riesz transforms associated to Schrödinger operator L = − + V on R n , n ≥ 3, where V is non-zero, nonnegative and belongs to the reverse Hölder class B q for q > n 2 . We prove that if T 1 = (− + V ) −1 V, T 2 = (− + V ) −1/2 V 1/2 and T 3 = (− + V ) −1/2 ∇, then the commutators [b, T j ], (j = 1, 2, 3) are compact on L p (R n ) when p ranges in an interval and b ∈ V M O(R n ).
doi:10.4310/pamq.2012.v8.n3.a7 fatcat:z3z2ry3bhzabzjcl3ntzcqdvkq