The Riemann-Hilbert boundary value problem for generalized analytic functions in Smirnov classes

Klimentov S. B.
Vladikavkaz Mathematical Journal 2012. Vol. 14. Issue 3.

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].

Keywords: Riemann--Hilbert boundary value problem, generalized analytic functions, Smirnov classes

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