New Hardy Spaces of Musielak-Orlicz Type and Boundedness of Sublinear Operators
New Hardy Spaces of Musielak-Orlicz Type and Boundedness of Sublinear Operators
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DOI：
10.1007/s00020-013-2111-z
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发表时间：
2014-01-01
影响因子：
0.8
通讯作者：
Luong Dang Ky
中科院分区：
文献类型：
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作者：
Luong Dang Ky
我们引入了一类新的Hardy空间，称为Musielak-Orlicz型Hardy空间，它推广了Janson的Hardy-Orlicz空间和Garcia-Cuerva、Stromberg和Torchinsky的加权Hardy空间。这里，是这样的函数，它是Orlicz函数并且是Muckenoupt权重。函数f属于当且仅当它的极大函数f*是可积的。例如，在对和中的函数乘积的描述中，这样的空间自然地出现(见Bonami等人)。载于《数学纯应用》97：230-241,2012)。我们通过极大极大函数刻画了这些空间，并建立了它们的原子分解。我们还刻画了它们的对偶空间。由Nakai和Yabuta刻画的逐点乘子类可视为的对偶，其中是与Musielak-Orlicz函数相关的Musielak-Orlicz型Hardy空间。进一步，在附加假设下，证明了如果T是次线性算子，并且将所有原子映射到拟Banach空间中的一致有界元，则T唯一地从到扩张到有界次线性算子。即使对于经典的Hardy-Orlicz空间，这些结果也是新的。
We introduce a new class of Hardy spaces , called Hardy spaces of Musielak-Orlicz type, which generalize the Hardy-Orlicz spaces of Janson and the weighted Hardy spaces of Garcia-Cuerva, Stromberg, and Torchinsky. Here, is a function such that is an Orlicz function and is a Muckenhoupt weight. A function f belongs to if and only if its maximal function f* is so that is integrable. Such a space arises naturally for instance in the description of the product of functions in and respectively (see Bonami et al. in J Math Pure Appl 97:230-241, 2012). We characterize these spaces via the grand maximal function and establish their atomic decomposition. We characterize also their dual spaces. The class of pointwise multipliers for characterized by Nakai and Yabuta can be seen as the dual of where is the Hardy space of Musielak-Orlicz type related to the Musielak-Orlicz function . Furthermore, under additional assumption on we prove that if T is a sublinear operator and maps all atoms into uniformly bounded elements of a quasi-Banach space , then T uniquely extends to a bounded sublinear operator from to . These results are new even for the classical Hardy-Orlicz spaces on .