Abstract
We describe the growth of the naturally defined argument of a bounded analytic function in the unit disk in terms of the complete measure introduced by A. Grishin. As a consequence, we characterize the local behavior of a logarithm of an analytic function. We also find necessary and sufficient conditions for closeness of $\log f(z)$, $f\in H^\infty$, and the local concentration of the zeros of $f$.
Citation
Igor Chyzhykov. "Argument of bounded analytic functions and Frostman’s type conditions." Illinois J. Math. 53 (2) 515 - 531, Summer 2009. https://doi.org/10.1215/ijm/1266934790
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