The Kato problem for weighted elliptic and parabolic operators of higher order
Abstract
We solve the Kato square root problem for parabolic operators of arbitrary order 2m whose coefficients are allowed to depend on both space and time in a merely measurable way and possess boundedness and ellipticity controlled by a Muckenhoupt A2-weight. Notably, the proof applies to the weighted Kato problem within an elliptic framework.
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