Fredholmness of Singular Integral Operators with Complex Conjugation on Star-Like Curves with Cusps

The paper is devoted to studying the Fredholmness of operators from the Banach algebra B of singular integral operators with complex conjugation and slowly oscillating coefficients on the Lebesgue spaces L p ( Γ ) with p ∈ ( 1 , ∞ ) over star-like curves Γ with cusps. Applying reductions to a Banach algebra of Wiener–Hopf operators with slowly oscillating coefficients on weighted Lebesgue spaces over the half-line R + and a Banach algebra of convolution type operators with piecewise slowly oscillating coefficients on weighted Lebesgue spaces over the real line R , we construct a Fredholm symbol calculus for the Banach algebra B and establish a Fredholm criterion for the operators in B .