Mean square of the error term in the asymmetric many dimensional divisor problem

Let $ba=(a_1,a_2,ldots,a_k)$, where $a_j (j=1,ldots,k)$ are positive integers such that $a_1 leq a_2 leq cdots leq a_k$. Let $d(ba;n)=sum_{n_1^{a_1}cdots n_k^{a_k}=n}1$ and $Delta(ba;x)$ be the error term of the summatory function of $d(ba;n)$. In this paper we show an asymptotic formula of the mean square of $Delta(ba;x)$ under a certain condition. Furthermore, in the cases $k=2$ and 3, we give unconditional asymptotic formulas for these mean squares.