Ladner's Theorem states that if P ≠ NP, then there is an infinite hierarchy of complexity classes strictly containing P and strictly contained in NP. The proof uses the completeness of SAT under many-one reductions in NP. The hierarchy contains complexity classes constructed by a kind of diagonalization, each containing some language to which the languages in the lower classes are not many-one reducible.
This motivates my question:
Let C be a complexity class, and let D be a complexity class that strictly contains C. If D contains languages that are complete for some notion of reduction, does there exist an infinite hierarchy of complexity classes between C and D, with respect to the reduction?
More specifically, I would like to know if there are results known for D = P and C = LOGCFL or C = NC, for an appropriate notion of reduction.
Ladner's paper already includes Theorem 7 for space-bounded classes C, as Kaveh pointed out in an answer. In its strongest form this says: if NL ≠ NP then there is an infinite sequence of languages between NL and NP, of strictly increasing hardness. This is slightly more general than the usual version (Theorem 1), which is conditional on P ≠ NP. However, Ladner's paper only considers D = NP.