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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 174010, 8 pages
http://dx.doi.org/10.1155/2014/174010
Research Article

Lipschitz Spaces and Fractional Integral Operators Associated with Nonhomogeneous Metric Measure Spaces

Department of Mathematics, Xinjiang University, Urumqi 830046, China

Received 1 December 2013; Revised 3 April 2014; Accepted 5 April 2014; Published 17 April 2014

Academic Editor: S. A. Mohiuddine

Copyright © 2014 Jiang Zhou and Dinghuai 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

The fractional operator on nonhomogeneous metric measure spaces is introduced, which is a bounded operator from into the space . Moreover, the Lipschitz spaces on nonhomogeneous metric measure spaces are also introduced, which contain the classical Lipschitz spaces. The authors establish some equivalent characterizations for the Lipschitz spaces, and some results of the boundedness of fractional operator in Lipschitz spaces are also presented.