Functional Analysis and Applications Seminar 

01/06/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building
Alexei Karlovich, Centro de Análise Funcional e Aplicações, Lisboa

Semi-Fredholm singular integral operators with piecewise continuous coefficients on weighted variable Lebesgue spaces are Fredholm

Kokilashvili, Paatashvili, and Samko proved in 2005 that the Cauchy singular integral operator is bounded on variable Lebesgue spaces with Khvedelidze weights on arbitrary Carleson curves. We show that if the Carleson curve satisfies, in addition, a so-called logarithmic whirl condition at each point, then every semi-Fredholm operator in the Banach algebra of singular integral operators with matrix piecesise continuous coefficients is Fredholm.