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\begin{document}$$1\le p\le \infty $$\end{document} and α>0\documentclass[12pt]{minimal}
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\begin{document}$$\alpha >0$$\end{document}, Besov spaces Bαp\documentclass[12pt]{minimal}
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\begin{document}$$B^p_\alpha $$\end{document} play a key role in the theory of α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}-Möbius invariant function spaces. In some sense, Bα1\documentclass[12pt]{minimal}
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\begin{document}$$B^1_\alpha $$\end{document} is the minimal α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}-Möbius invariant function space, Bα2\documentclass[12pt]{minimal}
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\begin{document}$$B^2_\alpha $$\end{document} is the unique α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}-Möbius invariant Hilbert space, and Bα∞\documentclass[12pt]{minimal}
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\begin{document}$$B^\infty _\alpha $$\end{document} is the maximal α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}-Möbius invariant function space. In this paper, under the α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}-Möbius invariant pairing and by the space Bα∞\documentclass[12pt]{minimal}
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\begin{document}$$B^\infty _\alpha $$\end{document}, we identify the predual and dual spaces of Bα1\documentclass[12pt]{minimal}
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\begin{document}$$B^1_\alpha $$\end{document}. In particular, the corresponding identifications are isometric isomorphisms. The duality theorem via the α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}-Möbius invariant pairing for Bαp\documentclass[12pt]{minimal}
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\begin{document}$$B^p_\alpha $$\end{document} with p>1\documentclass[12pt]{minimal}
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\begin{document}$$p>1$$\end{document} is also given.
