Banach algebras of singular integral operators with piecewise continuous coefficients. General contour and weight

Abstract

The Banach algebra generated by one-dimensional linear singular integral operators with matrix valued piecewise continuous coefficients in the spaceLp(Γ,ρ) with an arbitrary weight ρ is studied. The contour Γ consists of a finite number of closed curves and open arcs with satisfy the Carleson condition. The contour may have a finite number of points of selfintersection. The symbol calculus in this algebra is the main result of the paper.