The algebra of singular operators with terminal symbol on a piecewise smooth curve. II: Basic constructions (Q1603168)

This is the second part of the paper [ibid. 36, 1337-1347 (2000; Zbl 1024.47030), see the preceding review]. Singular integral operators on a piecewise smooth curve are under consideration. The terminal symbol is calculated and multiplicators of the corresponding Banach algebra of operators are described. On this basis, the Fredholm theory of these operators on weighted \(L_p\)- and \(C^{\mu}\)-type spaces is developed. The results extend those presented in \textit{A. P. Soldatov} [``One-dimensional singular operators and boundary value problems in function theory'' (Russian) (Moscow) (1991; Zbl 0774.47025)].