ABOUT ONE OF WEIGHT CLASSES OF SUBHARMONIC FUNCTIONS
Subharmonic functions introduced in the early twentieth century by F. Hartogs and F. Riesz, are applied in many areas nowadays. Special attention is paid to these classes of functions in complex and real analysis, in potential theory and mathematical physics. From the analytical works, the descriptions were obtained for classes of subharmonic in a plane functions characterized by exponential growth at infinity. The question on the validity of the same parametric representation for the weight classes allowing stronger growth at infinity arises in the theory of entire and meromorphic functions. The author of the article discusses the class of subharmonic in a plane functions with the Nevanlinna characteristic, which is integrable with an exponential weight in the complex plane, as well as studies the representation measures of the functions of this class and derives a necessary and sufficient condition for such measures. Proof of claims is carried out using the methods of complex and functional analysis. Based on the factors of the modified works by K. Weierstrass, potentials were constructed, which play a leading role in the study. Auxiliary assertions are formulated in the form of lemmas proving the main result.