On certain analytic (Nevanlinna) functions (Q1061261)

In the class \(N_ 1=\{\phi:\) \(\phi (z)=\int^{1}_{-1}z(1-tz)^{- 1}d\mu (t)\), \(\mu\) a probability measure\(\}\) of functions analytic in \(| z| <1\) the authors find bounds for \(| \phi |\), \(| \phi '|\), Im \(\phi\), arg \(\phi\), arg \(\phi\) (z)/z, arg \(\phi\) '(z), \(\int | \phi |^ p\), \(\int | \phi '|^ p\). Many of these are improvements on results of \textit{L. E. Dunduchenko} [Bulgar. Akad. Nauk Izv. Mat. Inst. 5, 35-41 (1961)].