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. 
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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/

[1] Srebro U., Yakubov E.H., “$\mu$-Homeomorphisms”, Contemp. Math., 211, 1997, 473–479 | DOI | MR | Zbl

[2] Gutlyanskii V., Ryazanov V., Srebro U., Yakubov E., The Beltrami equation, v. 1, Springer, Berlin, 2011 | MR

[3] Boyarskii B.V., “Gomeomorfnye resheniya sistem Beltrami”, Dokl. AN SSSR, 102:4 (1955), 661–664 | MR

[4] Boyarskii B.V., “Obobschennye resheniya sistemy differentsialnykh uravnenii pervogo poryadka ellipticheskogo tipa s razryvnymi koeffitsientami”, Matem. sb., 43 (86):4 (1957), 451–503

[5] Alhfors L., Lectures on quassiconformal mappings, Springer, Toronto–New Jork–London, 1966 | MR

[6] Vekua I.N., Obobschennye analiticheskie funktsii, Nauka, M., 1988

[7] Sadullaev A., Zhabborov N.M., “On a class of A-analytic functions”, Zhurn. SFU Ser. Matem. i fiz., 9:3 (2016), 374–383 | MR

[8] Salimova A.E., “Versiya teoremy Malyavena–Rubela dlya tselykh funktsii eksponentsialnogo tipa s kornyami okolo mnimoi osi”, Izv. vuzov. Matem., 2022, no. 8, 46–55 | Zbl

[9] Zhuraeva U.Yu., “Teoremy tipa Fragmena–Lindelefa dlya bigarmonicheskikh funktsii”, Izv. vuzov. Matem., 2022, no. 10, 42–65

[10] Zhabborov N.M., Otaboev T.U., “Analog integralnoi formuly Koshi dlya $A$-analiticheskikh funktsii”, Uzbeksk. matem. zhurn., 2016, no. 4, 50–59 | MR

[11] Zhabborov N.M., Otaboev T.U., Khursanov Sh.Ya., “Neravenstvo Shvartsa i formula Shvartsa dlya $A$-analiticheskikh funktsii”, Sovremen. matem. Fundament. napravl., 64, no. 4, 2018, 637–649