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Variational characterization of Hp

Published online by Cambridge University Press:  15 January 2019

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

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 $p\in (((n)/({n+1})),1]$.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2019 

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