Let $SUBLOG = DSPACE(o(\log(n)) \setminus DSPACE(O(1))$ be the set of languages decidable with less than logarithmic space, but more than a constant amount of space, on a multi-tape Turing machine with a read-only input tape.
We have good implicit characterizations of constant space, i.e. regular languages, such as regular expressions or finite-state machines. Likewise, many circuit classes or larger space/time classes have good implicit characterizations: constant-depth circuit classes have logical representations using quantifier types that correspond to the gates, while $L$ and $P$ have characterizations due to Jones and Bellantoni/Cook respectively as restricted programming languages.
Are there any good known implicit characterizations / descriptive complexity approaches to sublogarithmic space (specifically any subclasses of $SUBLOG$)? I know the lack of robustness of sublogarithmic space makes such a characterization unlikely, so I'd be happy even with partial results in this direction.