N. M. Zhabborov, B. E. Husenov, “Fatou's theorem for <nobr>$A(z)$</nobr>-analytic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, Number 7,Pages <nobr>13

Fatou's theorem for $A(z)$-analytic functions

N. M. Zhabborov^a, B. E. Husenov^b

^a Belorussian-Uzbek joint intersectoral institute of applied technical qualifications in Tashkent, 4 Karamurt-1 str., Kibraisky district, Tashkent region, 100071 Republic of Uzbekistan
^b Bukhara State University, 11 Muhammad Ikbal str., Bukhara, 705018 Republic of Uzbekistan

Abstract: 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.

UDC: 517.55

Received: 29.03.2023
Revised: 07.05.2023
Accepted: 29.05.2023

DOI: 10.26907/0021-3446-2023-7-13-22