Spread of functions meromorphic in the disc
Let \(f\) be a function meromorphic in the unit disc. The paper contains estimations from below for the upper limits (as \(r\to 1)\) of the following quantities: \[ (1-r)^{-1}\text{ mes}(t:\log| f(re^{it})|>qT(r,f)/(1-r)), \] \[ (1-r)^{-1}\text{ mes}(t:\log| f(re^{it})|>qT(r,f)), \] \[ (1-r)^{-1}\text{ mes}(t:\log| f(re^{it})|>q \log M(r,f)), \] where \(0\leq q<\infty\); \(T\) and \(M\) are standard notations of the Nevanlinna theory. These estimations are obtained in terms of the lower order of the function \(f\) and the quantities \(\delta(\infty,f)\), \(\beta(\infty,f)\), \(\hat\beta(\infty,f)\), where \(\delta\) is the Nevanlinna deficiency and the \(\beta\)'s are the Petrenko deviations [\textit{V. P. Petrenko}, Entire curves (Russian) (1984; Zbl 0591.30030)].
scientific article; zbMATH DE number 56614