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arXiv · 2503.01636

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

Guoming Zhang
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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 $A_{2}-$weight. Notably, the proof applies to the weighted Kato problem within an elliptic framework.

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Guoming Zhang. 2025-03-03. The Kato problem for weighted elliptic and parabolic operators of higher order. https://arxiv.org/abs/2503.01636

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