- Citation:
- Karlovich, Alexei Yu. "Algebras of singular integral operators with piecewise continuous coefficients on weighted Nakano spaces." The Extended Field of Operator Theory. Operator Theory: Advances and Applications, 171. Ed. Michael A. Dritschel. Basel: Birkhäuser, 2007. 171-188.

### Abstract:

We find Fredholm criteria and a formula for the index of an arbitrary operator in the Banach algebra of singular integral operators with piecewise continuous coefficients on Nakano spaces (generalized Lebesgue spaces with variable exponent) with Khvedelidze weights over either Lyapunov curves or Radon curves without cusps. These results ``localize'' the Gohberg-Krupnik Fredhohn theory with respect to the variable exponent.

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