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Fall and Winter 2016 Weighted local Hardy spaces associated to Schrödinger operators
Hua Zhu, Lin Tang
Illinois J. Math. 60(3-4): 687-738 (Fall and Winter 2016). DOI: 10.1215/ijm/1506067287

Abstract

In this paper, we characterize the weighted local Hardy spaces $h^{p}_{\rho}(\omega)$ related to the critical radius function $\rho$ and weights $\omega\in A_{\infty}^{\rho,\infty}(\mathbb{R}^{n})$ which locally behave as Muckenhoupt’s weights and actually include them, by the local vertical maximal function, the local nontangential maximal function and the atomic decomposition. Then, we establish the equivalence of the weighted local Hardy space $h^{1}_{\rho}(\omega)$ and the weighted Hardy space $H^{1}_{\mathcal{L}}(\omega)$ associated to Schrödinger operators $\mathcal{L}$ with $\omega\in A_{1}^{\rho,\infty}(\mathbb{R}^{n})$. By the atomic characterization, we also prove the existence of finite atomic decompositions associated with $h^{p}_{\rho}(\omega)$. Furthermore, we establish boundedness in $h^{p}_{\rho}(\omega)$ of quasi-Banach-valued sublinear operators.

Citation

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Hua Zhu. Lin Tang. "Weighted local Hardy spaces associated to Schrödinger operators." Illinois J. Math. 60 (3-4) 687 - 738, Fall and Winter 2016. https://doi.org/10.1215/ijm/1506067287

Information

Received: 16 May 2016; Revised: 6 June 2017; Published: Fall and Winter 2016
First available in Project Euclid: 22 September 2017

zbMATH: 1376.42029
MathSciNet: MR3705443
Digital Object Identifier: 10.1215/ijm/1506067287

Subjects:
Primary: 42B30
Secondary: 42B20, 42B25

Rights: Copyright © 2016 University of Illinois at Urbana-Champaign

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Vol.60 • No. 3-4 • Fall and Winter 2016
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