On the boundedness of the Hardy operator in the weighted space BMO

The result of Golubov [5, Theorem 2] on the boundedness of the Hardy-Littlewood operator $$ mathcal{B}f(x): = frac{1} {x}int_0^x {f(t)} dt $$ in the space BMO(?) is well known. The author of the present paper solves the analogous problem in the weighted space BMO on the semi-axis ?₊ for the operator $$ T_w f(x): = frac{1} {{W(x)}}int_0^x {f(t)w(t)} dt $$ and also in the classical space BMO(?₊) for a class of integral operators involving, for example, the Riemann-Liouville fractional integral.