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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