The index of singular integral operators in reflexive Orlicz spaces

Citation:
Karlovich, Alexei Yu. "The index of singular integral operators in reflexive Orlicz spaces." Mathematical Notes. 64.3 (1998): 330-341.

Abstract:

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.

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