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 Vladikavkaz. Mat. Zh., 2012, Volume 14, Number 3, Pages 63–73 (Mi vmj428)

This article is cited in 4 scientific papers (total in 4 papers)

The Riemann–Hhilbert boundary value problem for generalized analytic functions in Smirnov classes

S. B. Klimentovab

a Southern Federal University, Russia, Rostov-on-Don
b South Mathematical Institute of VSC RAS, Russia, Vladikavkaz

Abstract: Under study is the Riemann–Hilbert boundary value problem for generalized analytic functions of a Smirnov class in a bounded simply connected domain whose boundary is a Lyapunov curve or a Radon curve without cusps. The coefficient of the boundary value condition is assumed continuous and perturbed by a bounded measurable function or continuous and perturbed by a bounded variation function. The paper uses the special representation for generalized analytic functions of Smirnov classes from the author's paper [16], which reduces the problem to that for holomorphic functions. The problem for the holomorphic functions was under study in the author's papers [1,2].

Key words: Riemann–Hilbert boundary value problem, generalized analytic functions, Smirnov classes.

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UDC: 517.518.234+517.548.3
Received: 28.08.2011

Citation: S. B. Klimentov, “The Riemann–Hhilbert boundary value problem for generalized analytic functions in Smirnov classes”, Vladikavkaz. Mat. Zh., 14:3 (2012), 63–73

Citation in format AMSBIB
\Bibitem{Kli12} \by S.~B.~Klimentov \paper The Riemann--Hhilbert boundary value problem for generalized analytic functions in Smirnov classes \jour Vladikavkaz. Mat. Zh. \yr 2012 \vol 14 \issue 3 \pages 63--73 \mathnet{http://mi.mathnet.ru/vmj428} 

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This publication is cited in the following articles:
1. Kokilashvili V., Paatashvili V., “The Riemann Boundary Value Problem in Variable Exponent Smirnov Class of Generalized Analytic Functions”, Proc. A Razmadze Math. Inst., 169 (2015), 105–118
2. V. Paatashvili, “Certain properties of generalized analytic functions from Smirnov class with a variable exponent”, Mem. Differ. Equ. Math. Phys., 69 (2016), 77–91
3. V. Kokilashvili, V. Paatashvili, “On the Riemann-Hilbert boundary value problem for generalized analytic functions in the framework of variable exponent spaces”, Math. Meth. Appl. Sci., 40:18 (2017), 7267–7286
4. Pozzi E., “Hardy Spaces of Generalized Analytic Functions and Composition Operators”, Concr. Operators, 5:1 (2018), 9–23
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