Subharmonic functions on annuli. A two-parameter approach

Анотація

In the paper [1] it has been studied subharmonic functions in the annulus A_r={z: 1/r<|z|<r}, r > 1. In this paper a two-parameter approach for investigation of subharmonic functions in the annulus A_s,r={z: s<|z|<r}, s <1 < r, is suggested. The consideration of functions subharmonic in the annulus A_s,r allows to describe their behavior at approaching to the inner and outer boundary circles of such annulus. Nevanlinna characteristic of functions subharmonic in such annulus is introduced. A counterpart of Jensen’s theorem for subharmonic functions in such annulus is proved. An estimate of a subharmonic function maximum by its Nevanlinna characteristic is established.