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Journal of Function Spaces
Volume 2015, Article ID 823862, 11 pages
http://dx.doi.org/10.1155/2015/823862
Research Article

The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators

College of Mathematics and Econometrics, Hunan University, Changsha 410082, China

Received 21 July 2015; Accepted 22 October 2015

Academic Editor: Dashan Fan

Copyright © 2015 Hua Wang. 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

Let be a Schrödinger operator acting on , , where is a nonnegative locally integrable function on . In this paper, we will first define molecules for weighted Hardy spaces associated with and establish their molecular characterizations. Then, by using the atomic decomposition and molecular characterization of , we will show that the imaginary power is bounded on for , and the fractional integral operator is bounded from to , where , , and .