The Kato problem for weighted elliptic and parabolic systems of higher order

Abstract: We solve the Kato square root problem for parabolic $N\times N$ systems of arbitrary order $2m$ whose coefficients are allowed to depend on both space and time in a merely measurable way and possess ellipticity controlled by a Muckenhoupt $A_{2}-$weight. Notably, the proof applies to the weighted Kato problem within an elliptic framework.