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Variational characterization of Hp

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  15 January 2019

Honghai Liu
Honghai Liu*
Affiliation:
Henan Polytechnic University, Jiaozuo, China (hhliu@hpu.edu.cn)
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Abstract

In this paper, we obtain the variational characterization of Hardy space Hp for $p\in (((n)/({n+1})),1]$, and get estimates for the oscillation operator and the λ-jump operator associated with approximate identities acting on Hp for $p\in (((n)/({n+1})),1]$. Moreover, we give counterexamples to show that the oscillation and λ-jump associated with some approximate identity cannot be used to characterize Hp for $p\in (((n)/({n+1})),1]$.

Keywords

Hardy spacesvariation operatorsjump operatorsapproximate of identities

MSC classification

Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 42B30: $H^p$-spaces
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 5 , October 2019 , pp. 1123 - 1134
Copyright
Copyright © Royal Society of Edinburgh 2019 

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