Norm of the Bergman projection onto the Bloch space with $\mathcal{M}-$invariant gradient

The value of the operator norm of Bergman projections from $L^{\mathrm{\infty }}({\mathbb{B}}^n)$ to Bloch space is found in \cite{KalajMarkovic2014}. The authors of mentioned paper proposed the problem of calculating the norm of the same class of operators with different norm on the Bloch space - $\mathcal{M}$-invariant gradient. Here we prove that it has the conjectured value.