@inbook {7472, title = {Singular integral operators with flip and unbounded coefficients on rearrangement-invariant spaces}, booktitle = {Functional Analysis and its Applications. Proceedings of the international conference, dedicated to the 110th anniversary of Stefan Banach, Lviv National University, Lviv, Ukraine, May 28--31, 2002}, year = {2004}, pages = {123-131}, publisher = {Elsevier}, organization = {Elsevier}, address = {Amsterdam}, abstract = {

We prove Fredholm criteria for singular integral operators of the form
\[
P_++M_bP_-+M_uUP_-,
\]
where \(P_\pm\) are the Riesz projections, \(U\) is the flip operator, and \(M_b,M_u\) are operators of multiplication by functions \(b,u\), respectively, on a reflexive rearrangement-invariant space with nontrivial Boyd indices over the unit circle. We assume a priori that \(M_b\) is bounded, but \(M_u\) may be unbounded. The function \(u\) belongs to a class of, in general, unbounded functions that relates to the Douglas algebra \(H^\infty+C\).

}, url = {http://www.sciencedirect.com/science/article/pii/S0304020804801610}, author = {Karlovich, Alexei Yu.}, editor = {Kadets, V. and Zelazko, W.} }