Regularity for the second order Riesz transforms associated with Schrödinger operators on weighted BMO type spaces

Abstract

Let L = −Δ + V be a Schrödinger operator on ℝn, where V is a nonnegative potential satisfying the suitable reverse Hölder’s inequality. In this paper, we study the boundedness of the second order Riesz transforms such as L−1∇2 on the spaces of BMO type for weighted case. We generalized the known results to the weighted case.

Keywords

• Riesz transform
• Schrödinger operator
• BMO type space
• weights