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Abstract and Applied Analysis
Volume 2013, Article ID 281562, 10 pages
Research Article

Weighted Endpoint Estimates for Commutators of Riesz Transforms Associated with Schrödinger Operators

School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Received 14 May 2013; Accepted 1 October 2013

Academic Editor: Baoxiang Wang

Copyright © 2013 Yu Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 .