On Subharmonic Functions of the First Order with Restrictions on the Real Axis - Poedintseva, I. V. (Журнал математичної фізики, аналізу, геометрії, 2008)
Subharmonic functions v of the first proximate order ρ(r) with the integral _0^R t^1-ρ(t)(v(t)+v(-t))1+t^2dt bounded with respect to R are studied. This is an extension of a result by N.I. Akhiezer, who studied the case ρ(r)1, v(z)=|f(z)|, where f(z) is an entire function. Mathematics Subject Classification: 31A05.