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Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 483951, 13 pages
http://dx.doi.org/10.1155/2013/483951
Research Article

The Higher Order Riesz Transform and BMO Type Space Associated with Schrödinger Operators on Stratified Lie Groups

1School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
2Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 1 October 2013; Accepted 7 November 2013

Academic Editor: Yoshihiro Sawano

Copyright © 2013 Yu Liu and Jianfeng Dong. 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.

Abstract

Assume that is a stratified Lie group and is the homogeneous dimension of . Let be the sub-Laplacian on and a nonnegative potential belonging to certain reverse Hölder class for . Let be a Schrödinger operator on the stratified Lie group . In this paper, we prove the boundedness of some integral operators related to , such as , , and ( ) on the space BMOL(G).