The algebra of singular operators with terminal symbol on a piecewise smooth curve. I: Convolution type operators on a semiaxis (Q5951162)

Criteria for compactness for multiplicative convolution type integral operators on the half-line of the form \[ (Kf)\phi(t_0) = \int_{0}^{\infty} k(t_0,t)f \biggl(\frac{t_0}{t}\biggr) \phi(t)\frac{dt}{t},\quad t_0 > 0, \] are obtained in spaces of \(L_p\)- and \(C^{\mu}\)-type. The results extend those presented in the author's book \textit{A. P. Soldatov}, ``One-dimensional singular operators and boundary value problems in function theory'' (Russian) (Moscow) (1991; Zbl 0774.47025)]. For Part II, see the following review Zbl 1024.47031).