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The Kato square root
problem for weighted parabolic operators
Alireza Ataei, Moritz Egert and Kaj Nyström |
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Vol. 18 (2025), No. 1, 141–169
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Abstract |
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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 nonautonomous character of the operator. Hence, we can allow for degenerate ellipticity dictated by a spatial -weight, which has not been treated before in this context. |
Keywords
Kato square root problem, second-order parabolic operators,
Muckenhoupt weights, square function estimates, fractional
derivatives
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Mathematical Subject Classification
Primary: 35K10, 42B25, 42B37
Secondary: 26A33, 47B44
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Milestones
Received: 22 September 2022
Revised: 30 August 2023
Accepted: 19 September 2023
Published: 15 December 2024
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Authors |
| Alireza Ataei | |
| Department of Mathematics Uppsala University Uppsala Sweden |
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| Moritz Egert | |
| Fachbereich Mathematik TU Darmstadt Darmstadt Germany |
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| Kaj Nyström | |
| Department of Mathematics Uppsala University Uppsala Sweden |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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