## An estimate for weighted Hilbert transform via square functions

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- by S. Petermichl and S. Pott PDF
- Trans. Amer. Math. Soc.
**354**(2002), 1699-1703 Request permission

## Abstract:

We show that the norm of the Hilbert transform as an operator on the weighted space $L^2(w)$ is bounded by a constant multiple of the $3/2$ power of the $A_2$ constant of $w$, in other words by $c \sup _I (\langle \omega \rangle _I \langle \omega ^{-1} \rangle _I)^{3/2}$. We also give a short proof for sharp upper and lower bounds for the dyadic square function.## References

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## Additional Information

**S. Petermichl**- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027
- Address at time of publication: Institute of Advanced Studies, Princeton, New Jersey 08540
- MR Author ID: 662756
- Email: stefanie@math.msu.edu
**S. Pott**- Affiliation: Department of Mathematics, University of York, York YO10 5DD, UK
- Email: sp23@york.ac.uk
- Received by editor(s): August 15, 2001
- Published electronically: October 26, 2001
- Additional Notes: The second author gratefully acknowledges support by EPSRC and thanks the Mathematics Department at MSU for its hospitality
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**354**(2002), 1699-1703 - MSC (1991): Primary 42A50; Secondary 42A61
- DOI: https://doi.org/10.1090/S0002-9947-01-02938-5
- MathSciNet review: 1873024