О неточностях в «точных» оценках для бигломорфных выпуклых отображений

In this paper there is considered the family $K^{n}$, $n\in \mathbb{N}$ of all $f, f(0)=0, Df(0)=I$, which map biholomorphically the unit ball $\mathbb{B}^{n}$ onto convex domains in $\mathbb{C}^{n}$. Several authors generalized the well-known classical inequality $(1+|z|)^{-2}\le |f'(z)|\le (1-|z|)^{-2}, z\in \mathbb{B}^{1}$, onto $n$-dimensional case; they have also declared that their inequalities are exact. In fact, in many cases the statemements were false. The intention of the paper is to indicate such cases