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Variational characterizations of weighted Hardy spaces and weighted $BMO$ spaces

Part of: Harmonic analysis in several variables Special classes of linear operators

Published online by Cambridge University Press:  01 December 2021

Weichao Guo ,
Yongming Wen ,
Huoxiong Wu  and
Dongyong Yang
Weichao Guo
Affiliation:
School of Science, Jimei University, Xiamen 361021, China (weichaoguomath@gmail.com)
Yongming Wen*
Affiliation:
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China (wenyongmingxmu@163.com)
Huoxiong Wu
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, China (huoxwu@xmu.edu.cn; dyyang@xmu.edu.cn)
Dongyong Yang
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, China (huoxwu@xmu.edu.cn; dyyang@xmu.edu.cn)
*
*Corresponding author.
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Abstract

This paper obtains new characterizations of weighted Hardy spaces and certain weighted $BMO$ type spaces via the boundedness of variation operators associated with approximate identities and their commutators, respectively.

Keywords

Variation operatorsapproximate identitiesweighted Hardy spacesweighted BMO(ℝn) spaces

MSC classification

Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 42B30: $H^p$-spaces 42B35: Function spaces arising in harmonic analysis 47B47: Commutators, derivations, elementary operators, etc.
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 6 , December 2022 , pp. 1613 - 1632
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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