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Weighted-BMO and the Hilbert transform

Hui-Ming Jiang — 1991

Studia Mathematica

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 B M O w to B M O w .

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