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Square function estimates and the Kato problem for second order parabolic operators in Rn+1
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 293, 1-36 p.Article in journal (Refereed) Published
Abstract [en]

In [4] the Kato square root problem for second order complex uniformly elliptic operators of the form L = -div(A del f), with only bounded and measurable coefficients, was solved. The solution is a consequence of a square function estimate for the operator (1 + lambda L-2)(-1)lambda L. This and related square function estimates have recently spurred a wave of new and ground breaking results in the area of elliptic PDEs. In this paper we establish similar square function estimates for second order parabolic operators in Rn+1 of the form at partial derivative(t) + L paving the way for important developments in the area of parabolic PDEs.

Place, publisher, year, edition, pages
2016. Vol. 293, 1-36 p.
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URN: urn:nbn:se:uu:diva-263917DOI: 10.1016/j.aim.2016.02.006ISI: 000373093200001OAI: diva2:858720
Available from: 2015-10-04 Created: 2015-10-04 Last updated: 2016-05-11Bibliographically approved

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