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  • YUFEI LI (a1), YUFENG LU (a2) and TAO YU (a3)


Let $\unicode[STIX]{x1D711}$ be an analytic self-map of the unit disc. If $\unicode[STIX]{x1D711}$ is analytic in a neighbourhood of the closed unit disc, we give a precise formula for the essential norm of the composition operator $C_{\unicode[STIX]{x1D711}}$ on the weighted Dirichlet spaces ${\mathcal{D}}_{\unicode[STIX]{x1D6FC}}$ for $\unicode[STIX]{x1D6FC}>0$ . We also show that, for a univalent analytic self-map $\unicode[STIX]{x1D711}$ of $\mathbb{D}$ , if $\unicode[STIX]{x1D711}$ has an angular derivative at some point of $\unicode[STIX]{x2202}\mathbb{D}$ , then the essential norm of $C_{\unicode[STIX]{x1D711}}$ on the Dirichlet space is equal to one.


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This research is supported by NSFC grant no. 11671065. The third author is supported by the NSFC grant nos. 11271332 and 11431011.



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