Multiparameter Hardy space theory on Carnot-Carathéodory spaces and product spaces of homogeneous type

By Yongsheng Han, Ji Li, G. Lu. 2012

46 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/2e63a4c09660d901801a0c70d2b56ab7ef6f7944

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In Applied Mathematics

1. G. Lu
2. Eric T. Sawyer
3. Yongsheng Han
4. Ji Li
5. Lesley A. Ward
6. Nguyen Huong Lam
7. Dachun Yang
8. Tuomas Hytönen

Citations in the corpus

• Hardy space theory on spaces of homogeneous type via orthonormal wavelet bases (2015, methodology): “ Euclidean spaces in [H1], and on spaces of homogeneous type, where the quasi-metric dsatisfies the H¨older regularity condition (1.4) and the measure µsatisfies condition (1.5), in [HS]. See [HMY] and [HLL2], respectively, for spaces of test functions and distributions on spaces of homogeneous type w”
• FLAG HARDY SPACES AND MARCINKIEWICZ MULTIPLIERS ON THE HEISENBERG GROUP (2012, methodology): “However, all the details are included in the expanded version of this paper [Han et al. 2012].”