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Kato's square root problem in Banach spaces

Hytonen, Tuomas; McIntosh, Alan; Portal, Pierre


Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces Lp (Rn ; X) of X -valued functions on Rn. We characterize Kato's square root estimates {norm of matrix} sqrt(L) u {norm of matrix}p {minus tilde} {norm of matrix} ∇ u {norm of matrix}p and the H∞-functional calculus of L in terms of R-boundedness properties of the resolvent of L, when X is a Banach function lattice with the UMD property, or a noncommutative Lp space. To do so, we develop...[Show more]

CollectionsANU Research Publications
Date published: 2008
Type: Journal article
Source: Journal of Functional Analysis
DOI: 10.1016/j.jfa.2007.10.006


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