The index of singular integral operators in reflexive Orlicz spaces

We consider the Banach algebra $\mathfrak{A}$ of singular integral operators with matrix piecewise continuous coefficients in the reflexive Orlicz spaceL _M ⁿ (Γ). We assume that Γ belongs to a certain wide subclass of the class of Carleson curves; this subclass includes curves with cusps, as well as curves of the logarithmic spiral type. We obtain an index formula for an arbitrary operator from the algebra $L_M^n (\Gamma )$ in terms of the symbol of this operator.