Prove that a boolean function computable in T(n) by a RAM machine is in DTIME(T(n)^2)
You write in the comments:


  Since the address should be written in the tape by a $T(n)$-time Turing Machine, the size (i.e. string length) of the address can not exceed $O(T(n))$.


Can you use a similar argument to improve the bounds 


  [The] tape can be of size $O(T(n)^2)$ with $O(T(n))$ pairs while the address of each pair can be of size $O(T(n))$.


you mention in the question? You may need to remember what operations are possible in constant time on the RAM, that is using the precise definition the authors use.