The Kato problem for operators with weighted ellipticity

Cruz-Uribe SFO, David; Rios, Cristian

doi:10.1090/S0002-9947-2015-06131-5

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

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