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Deviation inequalities and moderate deviations for estimators of parameters in an Ornstein-Uhlenbeck process with linear drift.

Gao, Fuqing; Jiang, Hui — 2009

Electronic Communications in Probability [electronic only]

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 $L^{\infty}$ 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 $L_{w}^{\infty}$ . 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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