Abstract
In this paper, we give new characterizations of the boundedness and compactness of composition operators <TEX>$C_{\varphi}$</TEX> between Bloch type spaces in the unit ball <TEX>$\mathbb{B}^n$</TEX>, in terms of the power of the components of <TEX>${\varphi}$</TEX>, where <TEX>${\varphi}$</TEX> is a holomorphic self-map of <TEX>$\mathbb{B}^n$</TEX>.
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