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

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

2010-02-25

arxiv.org/abs/1002.4813v1

Mathematics

Functional Analysis

23 pages

Scientific paper

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.

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