Weighted endpoint estimates for commutators of Riesz transforms associated with Schrödinger operators
type: Item
instance of: scholarly article
title: Weighted endpoint estimates for commutators of Riesz transforms associated with Schrödinger operators
zbMATH Open document ID: 1293.35063
DOI: 10.1155/2013/281562
author: Yu Liu
author: Jielai Sheng
author: Lijuan Wang
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: Let \(L=-\Delta+V\) be a Schrödinger operator, where \(\Delta\) is the Laplacian on \(\mathbb R^n\) and the nonnegative potential \(V\) belongs to the reverse Hölder class \(B_{s_1}\) for some \(s_1\geq(n/2)\). Assume that \(\omega\in A_1(\mathbb R^n)\). Denote by \(H^1_L(\omega)\) the weighted Hardy space related to the Schrödinger operator \(L=-\Delta+V\). Let \(\mathcal R_b=[b,\mathcal R]\) be the commutator generated by a function \(b\in\mathrm{BMO}_\theta(\mathbb R^n)\) and the Riesz transform \(\mathcal R=\nabla(-\Delta+V)^{-(1/2)}\). Firstly, we show that the operator \(\mathcal R\) is bounded from \(L^1(\omega)\) into \(L^1_{\mathrm{weak}}(\omega)\). Secondly, we obtain the endpoint estimates for the commutator \([b,\mathcal R]\). Namely, it is bounded from the weighted Hardy space \(H^1_L(\omega)\) into \(L^1_{\mathrm{weak}}(\omega)\).
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 6306601
zbMATH Keywords: weighted Hardy space
Wikidata QID: Q58915801
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/281562
OpenAlex ID: W2103060433
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description: scientific article; zbMATH DE number 6306601