Lipschitz functions in the strengthened contour-solid problem and continuation of the derivative on the boundary (Q1070376)

The author considers functions f(z) which are analytic in G and continuous in \(\bar G,\) where G is a region of the plane whose boundary contains \(\geq 2\) points. He investigates consequences of the assumption that f satisfies a Lipschitz condition on \(\partial G\). (If \(\infty \in \bar G\), it is also necessary to assume strict growth conditions of f at \(\infty)\). The conclusion is that the same Lipschitz data transfers to \(z\in G\), and thus gives information on f'(z). This paper has substantial overlap with the article ''Analytic functions satisfying Hölder conditions on the boundary'', by \textit{F. W. Gehring}, \textit{W. K. Hayman} and \textit{A. Hinkkanen} [J. Approximation Theory 35, 243-249 (1982; Zbl 0487.41009)] although methods are somewhat different. The latter cited paper, however, also applies to the full Hölder scale of exponents.