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On the local Hölder boundary smoothness of an analytic function in the unit ball compared with the smoothness of its modulus. (English) Zbl 1436.32023

Summary: Local boundary smoothness of an analytic function \(f\) in the unit ball of \({\mathbb{C}}^n\) 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.

MSC:

32A40 Boundary behavior of holomorphic functions of several complex variables
26B35 Special properties of functions of several variables, Hölder conditions, etc.
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