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

Abstract

In this paper, we give a very simple proof of the main result of Dafni (Canad Math Bull 45:46--59, 2002) concerning with weak${}^{\ast }$-convergence in the local Hardy space $h^1({\mathbb{R}}^d)$.