## 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

## Abstract:

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 $L^{2}\left ( w\right )$.## References

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## Additional Information

**David Cruz-Uribe SFO**- Affiliation: Department of Mathematics, Trinity College, Hartford, Connecticut 06106
- MR Author ID: 329597
- Email: David.CruzUribe@trincoll.edu
**Cristian Rios**- Affiliation: Department of Mathematics, University of Calgary, Calgary, Alberta, Canada T2N 1N4
- Email: crios@ucalgary.ca
- 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: https://doi.org/10.1090/S0002-9947-2015-06131-5
- MathSciNet review: 3335399