Well-known are classical Hardy-Littlewood-Sobolev and Zygmund results, that for the Riesz potential \[ I^ \alpha f(x)=\int_{R^ n}| x- y|^{\alpha-n}f(y)dy,\quad 0\lambda}dx\leq c\left({c\over\lambda}\int_{R^ n}| f(x)| dx\right)^{1/(n-\alpha)} \tag{3} \] are valid. These statements were generalized in many directions; for historical notices and review of results see the book by \textit{S. G. Samko}, the reviewer and \textit{O. I. Marichev} [Integrals and derivatives of fractional order and some of their applications (1987; Zbl 0617.26004), \(\S\S29\)]. In particular, \textit{E. T. Sawyer} [Trans. Am. Math. Soc. 281, 339-345 (1984; Zbl 0539.42008)] proved the necessary and sufficient conditions for a two-weighted weak type \((p,q)\) estimate \[ \int_{| I^ \alpha f(x)|>\lambda}w(x)dx\leq\lambda^{-q}\left(\int_{R^ n}| f(x)|^ pv(x)dx \right)^{q/p},\quad 1