Multiparameter Hardy space theory on Carnot-Carathéodory spaces and product spaces of homogeneous type
Multiparameter Hardy space theory on Carnot-Carathéodory spaces and product spaces of homogeneous type
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DOI：
10.1090/s0002-9947-2012-05638-8
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发表时间：
2012-07
影响因子：
1.3
通讯作者：
Yongsheng Han;Ji Li;G. Lu
中科院分区：
文献类型：
--
作者：
Yongsheng Han;Ji Li;G. Lu
本文受内格尔和Stein工作的启发，在由满足Hormander有限秩条件的向量场构成的乘积Carnot-Caratheodory空间M = M1×· ··×Mn的背景下，发展了Lp（1 < p < ∞）理论.本文的主要目的是提供一种统一的方法来发展齐型积空间上的多参数哈代空间理论。该理论包括乘积哈代空间及其对偶、乘积BMO空间、奇异积分算子的有界性以及算子的Calderon-Zygmund分解和插值。作为结果，我们得到了内格尔和Stein（2004）所考虑的奇异积分算子的端点估计.事实上，我们将在齐型乘积空间的框架下发展我们的理论，这些空间只满足加倍条件和关于度量的一些正则性假设。我们的所有结果都是通过引入一定的Banach空间的测试函数和分布，发展离散Calderon恒等式和离散Littlewood-Paley-Stein理论。我们的方法不依赖于经典乘积哈代空间上奇异积分有界性证明的主要工具--覆盖引理。
This paper is inspired by the work of Nagel and Stein in which the Lp (1 < p < ∞) theory has been developed in the setting of the product Carnot-Caratheodory spaces M = M1×· · ·×Mn formed by vector fields satisfying Hormander’s finite rank condition. The main purpose of this paper is to provide a unified approach to develop the multiparameter Hardy space theory on product spaces of homogeneous type. This theory includes the product Hardy space, its dual, the product BMO space, the boundedness of singular integral operators and Calderon-Zygmund decomposition and interpolation of operators. As a consequence, we obtain the endpoint estimates for those singular integral operators considered by Nagel and Stein (2004). In fact, we will develop most of our theory in the framework of product spaces of homogeneous type which only satisfy the doubling condition and some regularity assumption on the metric. All of our results are established by introducing certain Banach spaces of test functions and distributions, developing discrete Calderon identity and discrete Littlewood-Paley-Stein theory. Our methods do not rely on the Journe-type covering lemma which was the main tool to prove the boundedness of singular integrals on the classical product Hardy spaces.