Weak factorizations of the Hardy space in terms of multilinear fractional integral operator

We give a constructive proof of the factorization theorem for the classical Hardy space in terms of fractional integral operator. Moreover, the result is extended to the multilinear case and weighted case. As an application, we obtain the characterization of $BMO$ via the weighted boundedness of com...

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Bibliographic Details
Main Authors Wang, Dinghuai, Zhu, Rongxiang
Format Journal Article
LanguageEnglish
Published 12.12.2021
Subjects
Mathematics - Classical Analysis and ODEs
Mathematics - Functional Analysis
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Summary:We give a constructive proof of the factorization theorem for the classical Hardy space in terms of fractional integral operator. Moreover, the result is extended to the multilinear case and weighted case. As an application, we obtain the characterization of $BMO$ via the weighted boundedness of commutators of the multilinear fractional integral operator, without individual conditions on the weights class.
DOI:10.48550/arxiv.2112.06249