- December 6, 2002 , Friday - 15h00 (Room 3.10):
A Class of Singular Integral Operators
with Flip and Unbounded Coefficients
on Rearrangement-Invariant Spaces
Alexei Karlovich
(Instituto Superior Técnico, U.T.L.)
Abstract.
We prove Fredholm criteria for singular integral operators
of the form P+aQ+bUQ, where P and Q are the Riesz projections,
U is the flip operator, on a reflexive rearrangement-invariant
space with nontrivial Boyd indices over the unit circle. We assume
a priori that a is bounded, but b may be unbounded. The function
b belongs to a class of, in general, unbounded functions that
relates to the Douglas algebra H-infinity+C. This result is
new even for Lebesgue spaces. It refines and generalizes some
results of Kravchenko, Lebre, Litvinchuk, and Teixeira published
in the Mathematische Nachrichten in 1995.
Seminars take place in Lisbon, I.S.T. -
Post Graduation Building
Webpage: http://www.math.ist.utl.pt/funcional
