Behavior of holomorphic functions in complex tangential directions in a domain of finite type in \({\mathbb{C}}^ n\) (Q1199357)

The author compares the behavior of holomorphic functions in complex tangential directions and all directions. He shows that if \(\Omega\) is a domain of finite type in \(\mathbb{C}^ n\) then the regularity in complex tangential directions of a holomorphic function in \(\Omega\) implies the regularity in all directions. He gives a pointwise inequality in both directions between the gradients and the complex tangential gradients. He also characterizes Besov, Sobolev and Lipschitz spaces of holomorphic functions by the behavior of complex tangential derivations.