## Annals of Functional Analysis

### A note on weak$^{*}$-convergence in $h^{1}(\mathbb{R}^{d})$

#### Abstract

We give a very simple proof of a result by Dafni that states that the weak$^{*}$-convergence is true in the local Hardy space $h^{1}(\mathbb{R}^{d})$.

#### Article information

Source
Ann. Funct. Anal., Volume 7, Number 4 (2016), 573-577.

Dates
Received: 21 January 2016
Accepted: 8 April 2016
First available in Project Euclid: 31 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.afa/1472659943

Digital Object Identifier
doi:10.1215/20088752-3661494

Mathematical Reviews number (MathSciNet)
MR3543149

Zentralblatt MATH identifier
1346.42022

Subjects
Primary: 42B30: $H^p$-spaces
Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions

Keywords
$H^{1}$ BMO VMO Banach–Alaoglu

#### Citation

Hung, Ha Duy; Huy, Duong Quoc; Ky, Luong Dang. A note on weak $^{*}$ -convergence in $h^{1}(\mathbb{R}^{d})$. Ann. Funct. Anal. 7 (2016), no. 4, 573--577. doi:10.1215/20088752-3661494. https://projecteuclid.org/euclid.afa/1472659943

#### References

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