Hardy spaces associated with different homogeneities and boundedness of composition operators
Hardy spaces associated with different homogeneities and boundedness of composition operators
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DOI：
10.4171/rmi/751
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发表时间：
2013-12
影响因子：
1.2
通讯作者：
Yongsheng Han;Chin-Cheng Lin;G. Lu;Zhuoping Ruan;E. Sawyer
中科院分区：
文献类型：
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作者：
Yongsheng Han;Chin-Cheng Lin;G. Lu;Zhuoping Ruan;E. Sawyer
众所周知，具有各向同性和非各向同性齐次的标准Calderon-Zygmund奇异积分算子分别在经典H(R)和非各向同性H(R)上有界。本文提出了一个新的Hardy空间理论，并证明了两个不同齐次的Calderon-Zygmund奇异积分算子的组合在这个新的Hardy空间上是有界的。有趣的是，这样的Hardy空间具有与两个奇异积分算子所产生的混合齐次性相关的多参数结构。Calderon-Zygmund分解和插值定理适用于这种新的Hardy空间。
It is well known that standard Calderon-Zygmund singular integral operators with the isotropic and non-isotropic homogeneities are bounded on the classical H(R) and non-isotropic H h(R ), respectively. In this paper, we develop a new Hardy space theory and prove that the composition of two Calderon-Zygmund singular integral operators with different homogeneities is bounded on this new Hardy space. It is interesting that such a Hardy space has surprisingly a multiparameter structure associated with the underlying mixed homogeneities arising from two singular integral operators under consideration. The Calderon-Zygmund decomposition and an interpolation theorem hold on such new Hardy spaces.