Conical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi

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.

28 pages; submitted for publication

References in corpus (2)

• Stochastic integration in UMD Banach spaces
• Quadratic estimates and functional calculi of perturbed Dirac operators

Cited by in corpus (18)

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• Fractional Vector-Valued Littlewood-Paley-Stein Theory for Semigroups
• Local Hardy Spaces of Differential Forms on Riemannian Manifolds
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• A note on maximal estimates for stochastic convolutions
• Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions
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• Weighted tent spaces with Whitney averages: factorization, interpolation and duality
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• Best constants in the vector-valued Littlewood-Paley-Stein theory
• On well-posedness of parabolic equations of Navier-Stokes type with BMO^{-1}(\R^n) data