Carleman’s Formula for $$\boldsymbol{A(z)}$$-Analytic Functions

In this paper, we investigate $$A(z)$$ -analytic functions, where $$A(z)$$ is a function that is antianalytic. The article demonstrates the existence of an $$A(z)$$ -harmonic measure at most points on the boundary of a lemniscate. The main contribution of this paper is the development of a new quenching function for $$A(z)$$ -analytic functions. This quenching function is used to derive Carleman formula for $$A(z)$$ -analytic functions in the Hardy class.