Let T_ 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 fmapstoWcdotThof on generalized Morrey spaces. Under some assumptions on ho, we obtain an inequality for WcdotTho, which can be viewed as an extension of Olsen's and Kurata-Nishigaki-Sugano's results
