Logarithmic Bloch spaces in the polydisc, endpoint results for Hankel operators and pointwise multipliers

We define two notions of Logarithmic Bloch space in the polydisc for which we provide equivalent definitions in terms of symbols of bounded Hankel operators. We also provide a full characterization of the pointwise multipliers between two different Bloch spaces of the unit polydisc

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

The value of the operator norm of Bergman projections from $L^{\infty}(\mathbb{B}^n)$ 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.Comment: 8 page