A two weight inequality for the fractional integral when $p=n/\alpha$

Let ${I_\alpha }$ be the fractional integral operator defined as

$${I_\alpha }f(x) = \int {f(y){{\left\vert {x - y} \right\vert}^{\alpha - n}}dy.}$$

Given a weight $w$ (resp. $\upsilon$), necessary and sufficient conditions are given for the existence of a nontrivial weight $\upsilon$ (resp. $w$) such that

$${\left\Vert {\upsilon {\chi _B}} \right\Vert _\infty }\frac{1}{{\... ...\left( {\int {{{\left\vert f \right\vert}^{n/\alpha }}w} } \right)^{\alpha /n}}$$

holds for any ball $B$ such that ${\left\Vert {v{\chi _B}} \right\Vert _\infty } > 0$.