Boundedness of fractional operators on $L\sp{p}$ spaces with different weights

Let ${T_\alpha }$ be either the fractional integral operator $\smallint f(y)\vert x - y{\vert^{\alpha - n}}\; dy$, or the fractional maximal operator $\sup \left\{ {{r^{\alpha - n}}{\smallint_{\vert x - y\vert < r}}\vert f(y)\vert dy:\,r > 0} \right\}$. Given a weight $w$ (resp. $\upsilon$), necessary and sufficient conditions are given for the existence of a nontrivial weight $\upsilon$ (resp. $w$) such that ${(\smallint \vert{T_\alpha }f{\vert^q}\upsilon \;dx)^{1/q}} \leqslant {(\smallint\vert f{\vert^p}w\;dx)^{1/p}}$ holds. Weak type substitutes in limiting cases are considered.