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.