A representation of a class of subharmonic functions in the upper half-plane of the complex plane

Background. The theory of subharmonic functions is constantly evolving and raises the interest of many researchers. At the beginning of last century by F. Riesz in their studies have demonstrated important links between the theory of subharmonic functions, potential theory. A special place in the theory of subharmonic functions is integral representations in classes of subharmonic functions in various fields. The aim of this paper is to consider the class of subgarmonic functions in the upper half-plane of the complex plane with the characteristic of the Nevanlinna from Lp-weighted spaces. Materials and methods. Methods of complex and functional analysis are used to prove the main result. The auxiliary statements formulated in the form of lemmas are used in the construction of the proof. Results. A complete description of the subgarmonic class in the upper half-plane of the complex plane of functions with the characteristic of the Nevanlinna from Lp-weighted spaces, which allow the representation of the sum of the potential and the harmonic function, is carried out. Conclusions. Problems concerning the description of different classes of analytic and subgarmonic functions were considered earlier, however, the methods of their proof allowed to obtain a solution with certain restrictions, for example, on the value of the parameter p. In this paper, we construct a parametric representation of the subgarmonic class in the upper half-plane of the complex plane of functions with the characteristic of the Nevanlinna from Lp-weight spaces for all the values of the parameter p.