Mellin pseudodifferential operators techniques in the theory of singular integral operators on some Carleson curves

We consider an algebra A p (Γ,ω) of singular integral operators with slowly oscillating bounded coefficients acting in L p (Γ,ω), 1 < p < ∞, where Γ is a composed Carleson curve with logarithmic whirl points and ω is a power weight. The local analysis of operators A ∈ A p (Γ,ω) at singular points of the contours is based on the Mellin pseudodifferential operators method. This method gives effective formulas for the local symbols. These formulas describe the influence on the local symbol of both the curve and the weight in an explicit form.