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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-10,
author = {Alexei Yu. Karlovich},
title = {Singular integral operators on Nakano spaces with weights having finite sets of discontinuities},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {143-166},
zbl = {1233.47024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-10}
}
Alexei Yu. Karlovich. Singular integral operators on Nakano spaces with weights having finite sets of discontinuities. Banach Center Publications, Tome 95 (2011) pp. 143-166. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-10/