Geodesic
Fatou's theorem for $A(z)$-analytic functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2023), pp. 13-22

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We consider $A(z)-$analytic functions in case when $A(z)$ is an 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.
Keywords: $A(z)$-analytic function, $A(z)$-lemniscate, “radial” convergence in $A(z)$-lemniscate, the complex Lipschitz condition for $A(z)$-analytic function, Fatou's theorem for $A(z)$-analytic function. 
@article{IVM_2023_7_a1,
     author = {N. M. Zhabborov and B. E. Husenov},
     title = {Fatou's theorem for $A(z)$-analytic functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {13--22},
     publisher = {mathdoc},
     number = {7},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_7_a1/}
}
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N. M. Zhabborov; B. E. Husenov. Fatou's theorem for $A(z)$-analytic functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2023), pp. 13-22. http://geodesic.mathdoc.fr/item/IVM_2023_7_a1/