Functional Analysis and Applications Seminar 

16/09/2005, 15:00 — 16:00 — Room P3.10, Mathematics Building
Alexei Karlovich, Universidade do Minho

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.