Fatou’s Theorem for A(z)-Analytic Functions

We consider $$A(z)$$ -analytic functions in case when $$A(z)$$ is anti-analytic function. This paper investigates the behavior near the boundary of the derivative of the function, $$A(z)$$ -analytic inside the $$A(z)$$ -lemniscate and with a bounded change of it at the boundary. Thus, this paper introduces the complex Lipschitz condition for $$A(z)$$ -analytic functions and proves Fatou’s theorem for $$A(z)$$ -analytic functions.