Singular integral operators with piecewise continuous coefficients in reflexive Orlicz spaces (Q1385912)

We describe criteria for the Fredholm property and formulas for evaluating the index of singular integral operators with piecewise continuous coefficients in reflexive Orlicz spaces on a smooth closed contour. As a corollary, the essential spectrum of the operator of singular integration with the Cauchy kernel in a reflexive Orlicz space on a smooth open contour is evaluated, which revealed a new feature, viz., the obtained spectrum has a nonzero plane measure, as distinct from the particular case of Lebesgue spaces.