Weighted-BMO and the Hilbert transform
Volume 100 / 1991
Studia Mathematica 100 (1991), 75-80
DOI: 10.4064/sm-100-1-75-80
Abstract
In 1967, E. M. Stein proved that the Hilbert transform is bounded from $L^∞$ to BMO. In 1976, Muckenhoupt and Wheeden gave an analogue of Stein's result. They gave a necessary and sufficient condition for the boundedness of the Hilbert transform from $L^∞_w$. We improve the results of Muckenhoupt and Wheeden's and give a necessary and sufficient condition for the boundedness of the Hilbert transform from $BMO_w$ to $BMO_w$.
