New Hardy Spaces of Musielak-Orlicz Type and Boundedness of Sublinear Operators

作者：Luong Dang Ky^*

来源：Integral Equations and Operator Theory, 2014, 78(1): 115-150.

DOI：10.1007/s00020-013-2111-z

• Muckenhoupt weights
• Musielak-Orlicz functions
• BMO-multipliers
• hardy spaces
• atomic decompositions
• Hardy-Orlicz spaces
• quasi-Banach spaces
• sublinear operators

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 .

• 出版日期2014-1