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Abstract and Applied Analysis
Volume 2013, Article ID 741050, 8 pages
Research Article

Nonvanishing Preservers and Compact Weighted Composition Operators between Spaces of Lipschitz Functions

1School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
2School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China
3Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li 32023, Taiwan

Received 14 June 2013; Accepted 9 September 2013

Academic Editor: Fabio M. Camilli

Copyright © 2013 Dongyang Chen 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.


We will give the -Lipschitz version of the Banach-Stone type theorems for lattice-valued -Lipschitz functions on some metric spaces. In particular, when and are bounded metric spaces, if is a nonvanishing preserver, then is a weighted composition operator , where is a Lipschitz homeomorphism. We also characterize the compact weighted composition operators between spaces of Lipschitz functions.