## Singular integral operators on Nakano spaces with weights having finite sets of discontinuities

Citation:
Karlovich, Alexei Yu. "Singular integral operators on Nakano spaces with weights having finite sets of discontinuities." Function spaces IX. Proceedings of the 9th international conference, Kraków, Poland, July 6–11, 2009. Banach Center Publications, 92. Eds. Henryk Hudzik, Grzegorz Lewicki, Julian Musielak, Marian Nowak, and Leszek Skrzypczak. Warszawa: Polish Academy of Sciences, Institute of Mathematics, 2011. 143-166.

### Abstract:

In 1968, Gohberg and Krupnik found a Fredholm criterion for singular integral operators of the form $$aP+bQ$$, where $$a,b$$ are piecewise continuous functions and $$P,Q$$ are complementary projections associated to the Cauchy singular integral operator, acting on Lebesgue spaces over Lyapunov curves. We extend this result to the case of Nakano spaces (also known as variable Lebesgue spaces) with certain weights having finite sets of discontinuities on arbitrary Carleson curves.