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 space $L_M^n(\Gamma)$. We assume that $\Gamma$ 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 $\mathfrak A$ in terms of the symbol of this operator.