On Subharmonic Functions of the First Order with Restrictions on the Real Axis

Анотація

Subharmonic functions $v$ of the first proximate order $\rho(r)$ with the integral $\displaystyle\int_0^R \frac{t^{1-\rho(t)}(v(t)+v(-t))}{1+t^2}dt$ bounded with respect to $R$ are studied. This is an extension of a result by N.I. Akhiezer, who studied the case $\rho(r)\equiv 1$, $v(z)=\ln |f(z)|$, where $f(z)$ is an entire function.

Mathematics Subject Classification: 31A05.