Duality of multi-parameter triebel-lizorkin spaces associated with the composition of two singular integral operators
Duality of multi-parameter triebel-lizorkin spaces associated with the composition of two singular integral operators
复制标题
与两个奇异积分算子的组合相关的多参数 triebel-lizorkin 空间的对偶性
DOI：
10.1090/tran/6576
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发表时间：
2016
影响因子：
1.3
通讯作者：
Lu Guozhen
中科院分区：
文献类型：
--
作者：
Ding Wei;Lu Guozhen
本文研究了多参数Triebel-Lizorkin空间的对偶理论，它与不同齐性的两个奇异积分算子的合成有关。Phong和Stein在1982年考虑了两个奇异算子的这种组合。因为，我们建立了这样的空间的对偶空间，并且对于我们证明。然后证明了两个齐性不同的Calderón-Zygmund奇异积分算子的合成在空间上的有界性。令人惊讶的是，这种对偶空间与经典的单参数Triebel-Lizorkin空间有本质的不同。我们的工作需要对具有不同齐性的两个奇异积分算子的组合的多参数结构所产生的基础几何进行更复杂的分析。因此，在单参数条件下，它比Triebel-Lizorkin空间的对偶结果更难处理。我们注意到，对于和，是与Rev.Mat中考虑的两个奇异算子的合成相关的Hardy空间。伊比罗亚岛。29(2013)，1127-1157。我们的工作似乎是首次在多参数环境下研究Triebel-Lizorkin空间的对偶性。参考文献
In this paper, we study the duality theory of the multi-parameter Triebel-Lizorkin spacesassociated with the composition of two singular integral operators onof different homogeneities. Such composition of two singular operators was considered by Phong and Stein in 1982. For, we establish the dual spaces of such spaces as, and forwe prove. We then prove the boundedness of the composition of two Calderón-Zygmund singular integral operators with different homogeneities on the spaces. Surprisingly, such dual spaces are substantially different from those for the classical one-parameter Triebel-Lizorkin spaces. Our work requires more complicated analysis associated with the underlying geometry generated by the multi-parameter structures of the composition of two singular integral operators with different homogeneities. Therefore, it is more difficult to deal with than the duality result of the Triebel-Lizorkin spaces in the one-paramter settings. We note that for,and,is the Hardy space associated with the composition of two singular operators considered in Rev. Mat. Iberoam. 29 (2013), 1127–1157. Our work appears to be the first effort on duality for Triebel-Lizorkin spaces in the multi-parameter setting. References