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.
