Geodesic
Composition operators between Bloch and $\mathrm{BMOA}$ spaces on polydisks
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 44, Tome 447 (2016), pp. 51-65

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Let $\varphi$ be a holomorphic map between polydisks. We characterize those $\varphi$ for which the composition operator $f\mapsto f\circ\varphi$ maps the Bloch space into the small $\mathrm{BMOA}$ space. 
@article{ZNSL_2016_447_a3,
     author = {E. S. Dubtsov},
     title = {Composition operators between {Bloch} and $\mathrm{BMOA}$ spaces on polydisks},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {51--65},
     publisher = {mathdoc},
     volume = {447},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_447_a3/}
}
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E. S. Dubtsov. Composition operators between Bloch and $\mathrm{BMOA}$ spaces on polydisks. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 44, Tome 447 (2016), pp. 51-65. http://geodesic.mathdoc.fr/item/ZNSL_2016_447_a3/