Setting and solving several factorization problems for integral operators

U +/- are unknown upper and lower Volterra operators. Classes of generalized Volterra operators U +/- are introduced such that I-U +/- are not necessarily invertible operators in the spaces of functions on (a,b) under consideration. ii combination of the method of non-linear factorization equations and a priori estimates brings forth new results on the existence and properties of the solution to this problem for k greater than or equal to 0: both in the subcritical case mu < 1 and in the critical case <mu> = 1, where mu = r(K) is the spectral radius of the operator K. In addition, the problem of non-Volterra factorization is posed and studied, when the kernels of U+ and U- vanish on some parts S- and S+ of the domain S = (a,b)(2) such that S+ boolean OR S- = S.