Analogue of the Carleman’s formula for $A(z)$-analytic functions

In this report, an analogue of the Carleman formula is proved for $A(z)$-analytic functions from the Hardy class. The idea of obtaining the Carleman formula and the concept of the Carleman function for $A(z)$-analytic functions from the Hardy class belongs to M.M.Lavrentiev. In the proof of Carleman’s formula, $A(z)$-harmonic functions and the Poisson formula in lemniscates $L(a; r)$, compactly belonging to the domain under consideration $D \subset C$, are used substantially.