Geodesic
The index of singular integral operators in reflexive Orlicz spaces
Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 383-396

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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. 
@article{MZM_1998_64_3_a5,
     author = {A. Yu. Karlovich},
     title = {The index of singular integral operators in reflexive {Orlicz} spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {383--396},
     publisher = {mathdoc},
     volume = {64},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a5/}
}
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A. Yu. Karlovich. The index of singular integral operators in reflexive Orlicz spaces. Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 383-396. http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a5/