Distribution properties of sequences generated by Q-additive functions with respect to Cantor representation of integers

In analogy to ordinary q-additive functions based on q-adic expansions one may use Cantor expansions with a Cantor base Q to define (strongly) Q-additive functions. This paper deals with distribution properties of multi-dimensional sequences which are generated by such Q-additive functions. If in each component we have the same Cantor base Q, then we show that uniform distribution already implies well distribution and we provide an if and only if condition under which such sequences are uniformly distributed modulo one. For different Cantor bases in the single coordinate directions the question for uniform distribution becomes much more involved. We give a criterion which is sufficient and, in the case of strongly Q-additive functions, also necessary.