Construction of convex mappings of \(p\)-balls in \(\mathbb{C}^2\) (Q1880497)

The authors consider biholomorphic mappings \(F\) of the \(p\)-ball \(B_p=\{ (z,w)\in\mathbb{C}^2 : | z| ^p+| w| ^p < 1 \}\), where \(2\leq p < \infty\). In particular, they find conditions under which functions of the form \(F(z,w)=(z+aw^k,w)\), where \(a\in\mathbb{C}\) and \(k\in\mathbb{N}\), and \(F(z,w)=(f(z),g(w))\), where \(f\) and \(g\) are mappings of the unit disk, map \(B_p\) onto convex domains in \(\mathbb{C}^2\).