# Weighted-BMO and the Hilbert transform

Studia Mathematica (1991)

- Volume: 100, Issue: 1, page 75-80
- ISSN: 0039-3223

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topJiang, Hui-Ming. "Weighted-BMO and the Hilbert transform." Studia Mathematica 100.1 (1991): 75-80. <http://eudml.org/doc/215874>.

@article{Jiang1991,

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 $BMO_w$.},

author = {Jiang, Hui-Ming},

journal = {Studia Mathematica},

keywords = {weighted bounded mean oscillation; Hilbert transform; bounded mean oscillation},

language = {eng},

number = {1},

pages = {75-80},

title = {Weighted-BMO and the Hilbert transform},

url = {http://eudml.org/doc/215874},

volume = {100},

year = {1991},

}

TY - JOUR

AU - Jiang, Hui-Ming

TI - Weighted-BMO and the Hilbert transform

JO - Studia Mathematica

PY - 1991

VL - 100

IS - 1

SP - 75

EP - 80

AB - 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 $BMO_w$.

LA - eng

KW - weighted bounded mean oscillation; Hilbert transform; bounded mean oscillation

UR - http://eudml.org/doc/215874

ER -

## References

top- [1] R. A. Hunt, B. Muckenhoupt and R. L. Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227-251. Zbl0262.44004
- [2] B. Muckenhoupt and R. L. Wheeden, Weighted bounded mean oscillation and the Hilbert transform, Studia Math. 54 (1976), 221-237. Zbl0318.26014
- [3] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, 1986.

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