Maximal and Area Integral Characterizations of Hardy-Sobolev Spaces in the Unit Ball of $\mathbb C^n$
Maximal and Area Integral Characterizations of Hardy-Sobolev Spaces in the Unit Ball of $\mathbb C^n$
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DOI：
10.4171/rmi/66
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发表时间：
1988-04
影响因子：
1.2
通讯作者：
P. Ahern;J. Bruna
中科院分区：
文献类型：
--
作者：
P. Ahern;J. Bruna
本文讨论了Cn的单位球中Hardy- sobolev空间的几个特征，即球中导数达到一定阶的全纯函数的空间属于经典Hardy空间。我们的一些表征是用极大函数，面积函数或Littlewood-Paley函数来描述的，这些函数只涉及复切导数。我们的结果的一个特例是只涉及复切导数的Hp本身的表征。
In this paper we deal with several characterizations of the Hardy-Sobolev spaces in the unit ball of Cn, that is, spaces of holomorphic functions in the ball whose derivatives up to a certain order belong to the classical Hardy spaces. Some of our characterizations are in terms of maximal functions, area functions or Littlewood-Paley functions involving only complex-tangential derivatives. A special case of our results is a characterization of Hp itself involving only complex-tangential derivatives.