Criteria for One-Sided Invertibility of a Functional Operator in Rearrangement-Invariant Spaces of Fundamental Type

Let γ be a simple open smooth curve and be an orientation-preserving diffeomorphism of α onto itself which has only two fixed points.Criteria for one-sided invertibility of thefunctional operator A = aI — bW, where a and b are continuous functions, I is the identity operator, W is the shift operator: (Wf ) (t) =fα (t)], in a reflexive rearrangement-invariant space of fundamental type X(γ) with nontrivial Boyd indices, are obtained.