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We will give the -Lipschitz version of the Banach-Stone type theoremsfor 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 compositionoperators between spaces of Lipschitz functions

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