On weak${}^{\ast }$-convergence in $H_L^1({\mathbb{R}}^d)$

Abstract

Let $L=-\Delta +V$ be a Schrödinger operator on ${\mathbb{R}}^d$, $d\ge 3$, where $V$ is a nonnegative function, $V\ne 0$, and belongs to the reverse Hölder class $R{H}_{d/2}$. In this paper, we prove a version of the classical theorem of Jones and Journé on weak${}^{\ast }$-convergence in the Hardy space $H_L^1({\mathbb{R}}^d)$.

Potential Anal. (to appear)