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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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The Kato problem for operators with weighted ellipticity
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by David Cruz-Uribe SFO and Cristian Rios PDF
Trans. Amer. Math. Soc. 367 (2015), 4727-4756 Request permission


We consider second order operators $\mathcal {L}_{w}=-w^{-1}\operatorname {div}\mathbf {A}_{w}\nabla$ with ellipticity controlled by a Muckemphout $A_{2}$ weight $w$. We prove that the Kato square root estimate $\left \Vert \mathcal {L} _{w}^{1/2}f\right \Vert _{L^{2}\left ( w\right ) }\approx \left \Vert \nabla f\right \Vert _{L^{2}\left ( w\right ) }$ holds in the weighted space $L^{2}\left ( w\right )$.
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Additional Information
  • David Cruz-Uribe SFO
  • Affiliation: Department of Mathematics, Trinity College, Hartford, Connecticut 06106
  • MR Author ID: 329597
  • Email:
  • Cristian Rios
  • Affiliation: Department of Mathematics, University of Calgary, Calgary, Alberta, Canada T2N 1N4
  • Email:
  • Received by editor(s): September 24, 2012
  • Received by editor(s) in revised form: January 6, 2013, March 9, 2013, March 10, 2013, March 11, 2013, and March 13, 2013
  • Published electronically: March 2, 2015
  • Additional Notes: The first author was partially supported by the Stewart-Dorwart faculty development fund at Trinity College
    The second author was supported by the Natural Sciences and Engineering Research Council of Canada
  • © Copyright 2015 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 4727-4756
  • MSC (2010): Primary 35J15, 35J25, 35J70, 35D30, 47D06, 35B30, 31B10, 35B45
  • DOI:
  • MathSciNet review: 3335399