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 Bf(x) := 1/x integral(x)(0)f(x)dt in the space BMO(R) is well known. The author of the present paper solves the analogous problem in the weighted space BMO on the semi-axis R(+) for the operator T(w)f(x) := 1/W(x) integral(x)(0)f(t)w(t)dt, and also in the classical space BMO(R(+)) for a class of integral operators involving, for example, the Riemann-Liouville fractional integral.