Skip navigation
Skip navigation

Kato's square root problem in Banach spaces

Hytonen, Tuomas; McIntosh, Alan; Portal, Pierre

Description

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]

dc.contributor.authorHytonen, Tuomas
dc.contributor.authorMcIntosh, Alan
dc.contributor.authorPortal, Pierre
dc.date.accessioned2015-12-07T22:25:48Z
dc.identifier.issn0022-1236
dc.identifier.urihttp://hdl.handle.net/1885/21463
dc.description.abstractLet 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 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 Lp theory of square roots of elliptic operators, as well as an Lp version of Carleson's inequality.
dc.publisherAcademic Press
dc.sourceJournal of Functional Analysis
dc.subjectKeywords: Carleson's inequality; Elliptic operators with bounded measurable coefficients; H8-functional calculus; Kato's square root problem; Maximal function; UMD spaces; Vector-valued harmonic analysis
dc.titleKato's square root problem in Banach spaces
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume254
dc.date.issued2008
local.identifier.absfor010106 - Lie Groups, Harmonic and Fourier Analysis
local.identifier.ariespublicationu4085724xPUB17
local.type.statusPublished Version
local.contributor.affiliationHytonen, Tuomas, University of Helsinki
local.contributor.affiliationMcIntosh, Alan, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationPortal, Pierre, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.startpage675
local.bibliographicCitation.lastpage726
local.identifier.doi10.1016/j.jfa.2007.10.006
dc.date.updated2015-12-07T09:41:18Z
local.identifier.scopusID2-s2.0-37449028714
local.identifier.thomsonID000252998200004
CollectionsANU Research Publications

Download

File Description SizeFormat Image
01_Hytonen_Kato's_square_root_problem_in_2008.pdf419.97 kBAdobe PDF    Request a copy


Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.

Updated:  19 May 2020/ Responsible Officer:  University Librarian/ Page Contact:  Library Systems & Web Coordinator