Kato's square root problem in Banach spaces
| dc.creator | Hytonen, Tuomas | |
| dc.creator | McIntosh, Alan | |
| dc.creator | Portal, Pierre | |
| dc.date | 2007-03-01 | |
| dc.date.accessioned | 2026-07-07T07:49:33Z | |
| dc.date.available | 2026-07-07T07:49:33Z | |
| dc.description | Let $L$ be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces $L^{p}(R^{n};X)$ of $X$-valued functions on $R^n$. We characterize Kato's square root estimates $\|\sqrt{L}u\|_{p} \eqsim \|\nabla u\|_{p}$ and the $H^{\infty}$-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 $L^{p}$ space. To do so, we develop various vector-valued analogues of classical objects in Harmonic Analysis, including a maximal function for Bochner spaces. In the special case $X=C$, we get a new approach to the $L^p$ theory of square roots of elliptic operators, as well as an $L^{p}$ version of Carleson's inequality. | |
| dc.description | 44 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703012 | |
| dc.identifier | http://arxiv.org/abs/math/0703012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124895 | |
| dc.subject | Functional Analysis | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 46B09; 46E40; 47A60; 47F05; 60G46 | |
| dc.title | Kato's square root problem in Banach spaces | |
| dc.type | text |