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This paper is devoted to the fractional Laplacian system with criticalexponents. We use the method of moving sphere to derive a Liouville Theorem,and then prove the solutions in R^n\{0} are radially symmetric andmonotonically decreasing radially. Together with blow up analysis and thePohozaev integral, we get the upper and lower bound of the local solutions inB_1\{0}. Our results is an extension of the classical work by Caffarelli et al[6, 7], Chen et al[16]

Liouville theorem and isolated singularity of fractional Laplacian system with critical exponents