Let $T_ho$ be the generalized fractional integral operator associated to a function $ho:(0,infty) o(0,infty)$, as defined in cite{Nak2}. For a function $W$ on $n$, we shall be interested in the boundedness of the multiplication operator $fmapsto W cdot T_ho f$ on generalized Morrey spaces. Under some assumptions on $ho$, we obtain an inequality for $W cdot T_ho$, which can be viewed as an extension of Olsen's and Kurata-Nishigaki-Sugano's results.

Keywords: Fractional integral operators, Hardy-Littlewood maximal operators, multiplication operators, Olsen inequality, Morrey spaces