  Let $A_{1},...A_{m}$ be a $n\times n$ invertible matrices. Let $0 \leq
\alpha<n$ and $0<\alpha_{i}<n$ such that $\alpha_1 + ... + \alpha_m = n-
\alpha$. We define%
  \begin{equation*}
  T_{\alpha}f(x)=\int \frac{1}{\left\vert x-A_{1}y\right\vert ^{\alpha
  _{1}}...\left\vert x-A_{m}y\right\vert ^{\alpha _{m}}}f(y)dy.
  \end{equation*}%
  In \cite{U-V} we obtained the boundedness of this operator from $L^{p(.)}(%
  \mathbb{R}^{n})$ into $L^{q(.)}(\mathbb{R}^{n})$ for $\frac{1}{q(.)}=\frac{1%
  }{p(.)}-\frac{\alpha }{n},$ in the case that $A_{i}$ is a power of certain
  fixed matrix $A~\ $and for exponent functions $p$ satisfying log-Holder
  conditions and $p(Ay)=p(y),$ $y\in \mathbb{R}^{n}$ $.$ We will show now that
  the hypothesis on $p$, in certain cases, is necessary for the boundedness of
$T_{\alpha}$ and we
  also prove the result for more general matrices $A_{i}.$ \footnote{Partially
supported by CONICET and SECYTUNC} \footnote{Math. subject classification:
42B25, 42B35.} \footnote{Key words: Variable Exponents, Fractional Integrals.}
