Abstract:
For a $f$ function holomorphic in an open set $G$ the paper solves problems on the relationships between its properties along $\partial G$, the boundary of $G$, on the one hand and along $\overline G$, the closure of $G$, on the other. The properties discussed are those that can be expressed in terms of the derivatives, moduli of continuity, and rates of decrease or increase of the function along $\overline G$ and along $\partial G$. The results are established for very wide classes of sets $G$ and majorants of the moduli of continuity. In particular, all the main results are true for every bounded simply-connected domain and any majorant of the type of a modulus of continuity. A number of problems posed in 1942 by Sewell are solved.
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