A sufficient condition is given on weight functions u and v on \mathbb R^n for which the fractional maximal operator M_s (0 ≤ s < n) defined by (M_sf)(x) = \mathrm {sup}_{Q \ni x} |Q|^{\frac{s}{n}–1} \int_Q | f (y) | dy or the fractional integral operator I_s (0 < s < n) defined by (I_s,f)(x) = \int_{\mathbb R^n} | x - y |^{s–n} f(y)dy is bounded from L^p (\mathbb R^n, vdx) into L^q(\mathbb R^n,udx) for 0 < q < p with p> 1 , where Q is a cube and n a non-negative integer.