Extending the Implicit Computational Complexity Approach to the sub-elementary time-space classes

A resource-free characterization of some complexity clesses is given, by means of predicative recursion and constructive diagonalization schemes, and of restrictions of substitution. Among other classes, we predicatively harmonize in the same hierarchy PTIMEF, the class E of the elementary functions, and the classes DTIMESPACEF(n^p, n^q)