Abstract of a paper by Tuomas Hytonen, Jan van Neerven, and Pierre Portal
This is an announcement for the paper "Conical square functions in UMD Banach spaces" by Tuomas Hytonen, Jan van Neerven, and Pierre Portal. Abstract: We study conical square function estimates for Banach-valued functions, and introduce a vector-valued analogue of the Coifman-Meyer-Stein tent spaces. Following recent work of Auscher-McIntosh-Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with a given bisectorial operator \(A\) with certain off-diagonal bounds, such that \(A\) always has a bounded \(H^{\infty}\)-functional calculus on these spaces. This provides a new way of proving functional calculus of \(A\) on the Bochner spaces \(L^p(\R^n;X)\) by checking appropriate conical square function estimates, and also a conical analogue of Bourgain's extension of the Littlewood-Paley theory to the UMD-valued context. Even when \(X=\C\), our approach gives refined \(p\)-dependent versions of known results. Archive classification: math.FA math.SP Mathematics Subject Classification: Primary: 46B09; Secondary: 42B25, 42B35, 46B09, 46E40, 47A60, 47F05 Remarks: 28 pages; submitted for publication The source file(s), tent/newsymbol.sty: 440 bytes tent/tent.bbl: 5616 bytes tent/tent.tex: 91867 bytes, is(are) stored in gzipped form as 0709.1350.tar.gz with size 29kb. The corresponding postcript file has gzipped size 167kb. Submitted from: J.M.A.M.vanNeerven@tudelft.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0709.1350 or http://arXiv.org/abs/0709.1350 or by email in unzipped form by transmitting an empty message with subject line uget 0709.1350 or in gzipped form by using subject line get 0709.1350 to: math@arXiv.org.
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Dale Alspach