Molecular Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications

Jun Liu, Long Huang and Chenlong Yue
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Jun Liu: School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
Long Huang: School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of the Guangdong Higher Education Institute, Guangzhou University, Guangzhou 510006, China
Chenlong Yue: School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China

Mathematics, 2021, vol. 9, issue 18, 1-24

Abstract: Let p ? ? ( 0 , ? ) n be an exponent vector and A be a general expansive matrix on R n . Let H A p ? ( R n ) be the anisotropic mixed-norm Hardy spaces associated with A defined via the non-tangential grand maximal function. In this article, using the known atomic characterization of H A p ? ( R n ) , the authors characterize this Hardy space via molecules with the best possible known decay. As an application, the authors establish a criterion on the boundedness of linear operators from H A p ? ( R n ) to itself, which is used to explore the boundedness of anisotropic Calderón–Zygmund operators on H A p ? ( R n ) . In addition, the boundedness of anisotropic Calderón–Zygmund operators from H A p ? ( R n ) to the mixed-norm Lebesgue space L p ? ( R n ) is also presented. The obtained boundedness of these operators positively answers a question mentioned by Cleanthous et al. All of these results are new, even for isotropic mixed-norm Hardy spaces on R n .

Keywords: expansive matrix; (mixed-norm) Hardy space; molecule; Calderón–Zygmund operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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