Algebras of singular integral operators on Nakano spaces with
Khvedelidze weights over Carleson curves with logarithmic whirl
points
We establish a Fredholm criterion for 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
Carleson curves with logarithmic whirl points. The proofs are based
on the boundedness result for the Cauchy singular integral operator
over arbitrary Carleson curves by Kokilashvili and Samko (presented
on OTFUSA 2005) and on the theory of submltiplicative functions
associated with curves, weights, and spaces developed by
Boettcher-Yu. Karlovich and further by the author.
