One-sided invertibility of binomial functional operators with a shift on rearrangement-invariant spaces

Let be an oriented Jordan smooth curve and a diffeomorphism of onto itself which has an arbitrary nonempty set of periodic points. We prove criteria for one-sided invertibility of the binomial functional operator wherea andb are continuous functions,I is the identity operator,W is the shift operator,Wf=fo, on a reflexive rearrangement-invariant spaceX() with Boyd indices _X , _X and Zippin indicesp _x,q _x satisfying inequalities Partially supported by F.C.T. (Portugal) grant PRAXIS XXI/BPD/22006/99.Partially supported by CONCACYT (México) grant, Cátedra Patrimonial, No. 990017-EX., nivel II.