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arXiv · 2209.11104

The Kato square root problem for weighted parabolic operators

Alireza Ataei·Moritz Egert·Kaj Nyström
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Abstract

We give a simplified and direct proof of the Kato square root estimate for parabolic operators with elliptic part in divergence form and coefficients possibly depending on space and time in a merely measurable way. The argument relies on the nowadays classical reduction to a quadratic estimate and a Carleson-type inequality. The precise organization of the estimates is different from earlier works. In particular, we succeed in separating space and time variables almost completely despite the non-autonomous character of the operator. Hence, we can allow for degenerate ellipticity dictated by a spatial $A_2$-weight, which has not been treated before in this context.

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Alireza Ataei, Moritz Egert, Kaj Nyström. 2022-09-22. The Kato square root problem for weighted parabolic operators. https://arxiv.org/abs/2209.11104

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