On the Local Holder Boundary Smoothness of an Analytic Function in the Unit Ball Compared with the Smoothness of Its Modulus

摘要

Local boundary smoothness of an analytic function f in the unit ball of Cn is compared to the smoothness of its modulus. We prove that in dimensions 2 and higher two different (and natural) conditions imposed on the zeros of f imply two different drops of its smoothness compared to the smoothness of |f|. We also show that some of the drops are the best possible.