Biholomorphically invariant families amongst Carleson class

Given α (0, 1), let T_α be the Carleson class of all meromorphic maps ƒ from the unit disk to the extended complex plane with

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where ƒ^# and dm mean the spherical derivative of ƒ and Lebesgue area measure on separately. And, let BIT_α and BIT_α,0 be the biholomorphically invariant families (amongst the Carleson class) consisting of those ƒ T_α with sup and lim_{|w| → 1} ||ƒ ο φ_w||_Tα = 0 respectively, where

. The main purpose of this article is to study BIT_α and BIT_α,0 via the Ahlfors-Shimizu characteristic, canonical factorization and bounded holomorphic maps.