Let be a Schrödinger operator, where is the laplacian on and the nonnegative potential belongs to the reverse Hölder class for some . Assume that . Denote by the weighted Hardy space related to the Schrödinger operator . Let be the commutator generated by a function and the Riesz transform . Firstly, we show that the operator is bounded from into . Secondly, we obtain the endpoint estimates for the commutator . Namely, it is bounded from the weighted Hardy space into .
"Weighted Endpoint Estimates for Commutators of Riesz Transforms Associated with Schrödinger Operators." Abstr. Appl. Anal. 2013 (SI26) 1 - 10, 2013. https://doi.org/10.1155/2013/281562