This article is cited in 4 papers

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

S. B. Klimentov<sup>ab

a</sup> 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.

UDC: 517.518.234+517.548.3

Received: 28.08.2011