Algebras of singular integral operators on compound contours with nodes that are logarithmic whirl points

This article treats the Banach algebra $\mathfrak M_p(\Gamma,\omega)$ generated by singular integral operators acting in the space $L_p(\Gamma,\omega)$, where $\omega$ is a power weight and $\Gamma$ a compound contour with nodes that are whirl points of logarithmic or weaker character, and by the operators of multiplication by bounded functions admitting discontinuities of the second kind. The algebra of symbols is described, and conditions in terms of the symbols are given for operators in $\mathfrak M_p(\Gamma,\omega)$ to be Fredholm. An essential role is played by theorems on local invertibility of pseudodifferential operators and by estimates of their local norms.