Riemann–Hilbert problem for variable exponent poly-Smirnov space on a piecewise Lyapunov boundary

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In this paper we study the Riemann–Hilbert problem for variable exponent poly-Smirnov space on a piecewise Lyapunov boundary. At first we introduce the poly-Smirnov function space with variable exponent, we obtain a decomposition of this space and verify the existence of the angular boundary value of function in this space. Then we investigate Dirichlet problem for poly-Smirnov function space. At last we consider Riemann–Hilbert problem for variable exponent poly-Smirnov space on a piecewise Lyapunov boundary. The method is transforming this problem into independent homogeneous Dirichlet problems, and the conditions of solvability as well as the explicit solutions are obtained.