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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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