Solvability of the Riemann–Hilbert boundary value problem with a two-side curling at infinity of order less than 1

摘要

We consider the Hilbert boundary value problem for the upper half-plane in the situation where its coefficients have countably many discontinuities of jump type and two-side curling at infinity.We obtain the general solution and describe completely its solvability in a special class of functions for the case where the index of the problem has power singularity of order lesser than 1.