Is there a limit on the length of queries for the oracle? Consider the class $L^A$ which contains all the languages that are decided by a deterministic Turing Machine that uses $O(log(n))$ space and that can make queries to an oracle that decides $A$. My question is what is the length of query that the machine can ask the oracle? Is it $O(log(n))$ or can it be polynomial in $n$ (where $n$ is the length of the input)?
It seems that the usual definition, following Ruzzo, Simon and Tompa, is as follows. The oracle tape is write-only but has no space constraints. It is erased after each oracle call. In addition, if the machine model were non-deterministic (which is not your case), then the oracle calling process would have to be deterministic.