2 results
Variational characterizations of weighted Hardy spaces and weighted $BMO$
spaces
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 6 / December 2022
- Published online by Cambridge University Press:
- 01 December 2021, pp. 1613-1632
- Print publication:
- December 2022
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- Article
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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.
Variational characterization of Hp
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 5 / October 2019
- Published online by Cambridge University Press:
- 15 January 2019, pp. 1123-1134
- Print publication:
- October 2019
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- Article
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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 
$p\in (((n)/({n+1})),1]$.
