Riesz transform characterization of weighted Hardy spaces associated to Schrödinger operators

Abstract

In this paper, we characterize the weighted local Hardy spaces $h_{\rho }^p(\omega )$ related to the critical radius function $\rho$ and weights $\omega \in A_1^{\rho ,\infty }({\mathbb{R}}^n)$ by localized Riesz transforms ${\hat{R}}_j$, in addition, we give a characterization of weighted Hardy spaces $H_{\mathcal{L}}^1(\omega )$ via Riesz tranforms associated to Schrödinger operator $\mathcal{L}$, where $Ł=-\Delta +V$ is a Schrödinger operator on ${\mathbb{R}}^n$ ($n\ge 3$) and $V$ is a nonnegative function satisfying the reverse Hölder inequality.

arXiv admin note: substantial text overlap with arXiv:1403.7641; and text overlap with arXiv:1107.3266, arXiv:1109.0099 by other authors

References in corpus (1)

• Weighted local Hardy spaces associated to Schrödinger operators