On Riemann boundary value problem (Q2716599)

There is considered a \({\mathbb C}\)-linear conjugation problem on the open rectifable arc \(\gamma\) with end-points \(a_1, a_2\), namely: to find a holomorphic function \(\Phi(z), z\in {\mathbb C}\setminus \overline{\gamma},\) having integrable singularities at \(a_k, k =1, 2,\) whose boundary values satisfy on \(\gamma\) the following linear relations NEWLINE\[NEWLINE \Phi^{+}(t) = G(t)\Phi^{-}(t) + g(t),\quad t\in \gamma. NEWLINE\]NEWLINE The solvability of this problem is studied in the case of oscillating coefficients and nonsmooth arc \(\gamma\). The oscillating behaviour of \(\text{arg} G\) and \(g\) is described in terms of asymptotics of certain generalized modulus of continuity.