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
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