Real-variable characterizations of Orlicz-slice Hardy spaces
Real-variable characterizations of Orlicz-slice Hardy spaces
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Orlicz 切片 Hardy 空间的实变量表征
DOI：
10.1142/s0219530518500318
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发表时间：
2019
影响因子：
2.2
通讯作者：
Wang Songbai
中科院分区：
文献类型：
--
作者：
Zhang Yangyang;Yang Dachun;Yuan Wen;Wang Songbai
本文首先引入了一类Orlicz-切片空间，它推广了Auscher等人最近研究的切片空间。在此基础上，利用径向极大函数，引入了一类新的Hardy型空间--Orlicz-Slice Hardy空间。这种新的Orlicz-Slice Hardy空间包含了Bonami和Feuto的Orlicz-Hardy空间的变体，以及de Paul Ablé和Feuto的Hardy-Meralgam空间作为特例。通过原子、分子、各种极大函数、泊松积分和Littlewood-Paley函数对它们进行了刻画。作为这些刻画的一个应用，作者建立了它们的有限原子刻画，进一步归纳了它们的对偶空间的刻画和次线性算子从这些Orlicz-Slice Hardy空间到拟Banach空间的有界性的一个判据。然后，应用这一判据，得到了[公式：见正文]型Calderón-Zygmund算子在这些Orlicz-Slice Hardy空间上的有界性。这些结果即使对于切片Hardy空间也是新的，而且对于Hardy-Meralgam空间，Littlewood-Paley函数刻画、[公式：见正文]型Calderón-Zygmund算子在这些Hardy类型空间上的有界性也是新的。
In this paper, the authors first introduce a class of Orlicz-slice spaces which generalize the slice spaces recently studied by Auscher et al. Based on these Orlicz-slice spaces, the authors then introduce a new kind of Hardy-type spaces, the Orlicz-slice Hardy spaces, via the radial maximal functions. This new scale of Orlicz-slice Hardy spaces contains the variant of the Orlicz–Hardy space of Bonami and Feuto as well as the Hardy-amalgam space of de Paul Ablé and Feuto as special cases. Their characterizations via the atom, the molecule, various maximal functions, the Poisson integral and the Littlewood–Paley functions are also obtained. As an application of these characterizations, the authors establish their finite atomic characterizations, which further induce a description of their dual spaces and a criterion on the boundedness of sublinear operators from these Orlicz-slice Hardy spaces into a quasi-Banach space. Then, applying this criterion, the authors obtain the boundedness of [Formula: see text]-type Calderón–Zygmund operators on these Orlicz-slice Hardy spaces. All these results are new even for slice Hardy spaces and, moreover, for Hardy-amalgam spaces, the Littlewood–Paley function characterizations, the dual spaces and the boundedness of [Formula: see text]-type Calderón–Zygmund operators on these Hardy-type spaces are also new.