On a Weighted Singular Integral Operator with Shifts and Slowly Oscillating Data

摘要

Let be orientation-preserving diffeomorphism (shifts) of onto itself with the only fixed points and and be the isometric shift operators on given by , , and where then the operator is Fredholm on and its index is equal to zero. Moreover, its regularizers are described. the weighted Cauchy singular integral operator. We prove that if a , a and c, d are continuous on R + and slowly oscillating at 0 and8, and then the operator (I -cUa) P+ 2 +(I -dUa) P-2 is Fredholm on L p(R +) and its index is equal to zero. Moreover, its regularizers are described.