UMD巴拿赫空间中圆锥平方函数的估计及其在H ∞泛函演算中的应用
Conical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi
摘要：
本文研究了Banach值函数的锥平方函数估计，并引入了Coifman-Meyer-Stein帐篷空间的向量值模拟.根据Auscher-McIntosh-Russ最近的工作，帐篷空间又被用来构造与给定的具有一定非对角界的二分算子（A）相关联的向量值Hardy空间的标度，使得（A）在这些空间上总是有界的（H^{ \infty }）-谓词演算。这提供了一种新的方法来证明（A）在Bochner空间（L^p（\R^n ;X））上的谓词演算，通过检查适当的圆锥平方函数估计，也是Bourgain将Littlewood-Paley理论推广到UMD值上下文中的一个圆锥模拟.即使当（X= \C）时，我们的方法也给出了已知结果的精确（p）依赖版本。
英文摘要：
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.
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