Multi-parameter Triebel-Lizorkin and Besov spaces associated with flag singular integrals
Multi-parameter Triebel-Lizorkin and Besov spaces associated with flag singular integrals
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DOI：
10.1007/s10114-010-8352-8
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发表时间：
2010-02
期刊：
影响因子：
--
通讯作者：
Yong Ding;G. Lu;Bolin Ma
中科院分区：
文献类型：
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作者：
Yong Ding;G. Lu;Bolin Ma
虽然单参数Triebel-Lizorkin和Besov空间理论在过去的几十年里得到了很好的发展，但这种理论的多参数对应理论仍然缺乏。本文的主要目的是在隐式多参数结构的背景下，利用离散Littlewood-Paley-Stein分析来发展多参数Triebel-Lizorkin和Besov空间的理论。这是由于Han和Lu最近的工作，他们建立了一个令人满意的多参数Littlewood-Paley-Stein分析理论和与Muller-Ricci-Stein和Nagel-Ricci-Stein研究的旗奇异积分算子相关的哈代空间.我们还证明了旗奇异积分算子在Triebel-Lizorkin空间和Besov空间上的有界性。本文的方法可以用来发展纯积情形下的多参数Triebel-Lizorkin和Besov空间的理论。
Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper is to develop a theory of multi-parameter Triebel-Lizorkin and Besov spaces using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the recent work of Han and Lu in which they established a satisfactory theory of multi-parameter Littlewood-Paley-Stein analysis and Hardy spaces associated with the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. We also prove the boundedness of flag singular integral operators on Triebel-Lizorkin space and Besov space. Our methods here can be applied to develop easily the theory of multi-parameter Triebel-Lizorkin and Besov spaces in the pure product setting.