A remark on the Fefferman-Phong inequality for \(2\times 2\) systems
type: Item
instance of: scholarly article
title: A remark on the Fefferman-Phong inequality for \(2\times 2\) systems
zbMATH Open document ID: 1219.35382
author: Alberto Parmeggiani
published in: Pure and Applied Mathematics Quarterly
publication date: 2011-06-07T00:00:00Z
review text: The author shows that the Fefferman-Phong inequality holds for \(2\times 2\) systems with elliptic trace provided an extra assumption is imposed on the off-diagonal terms. This condition is automatically fulfilled in the important case of off-diagonal terms that are either always real or always purely imaginary. The paper reviews the basic facts about the Weyl-Hörmander calculus. Then the theorems are stated and proved. The conditions on the off-diagonal terms are shown to be optimal by providing an example of system with positive-elliptic trace that does not satisfy either of the two conditions on hand and for which the Fefferman-Phong inequality does not hold.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35A30
zbMATH DE Number: 5904816
zbMATH Keywords: lower bounds
zbMATH Keywords: systems of pseudodifferential operators
zbMATH Keywords: Fefferman-Phong inequality
MaRDI profile type: Publication
full work available at URL: pamq.2010.v6.n4.a7
OpenAlex ID: W2332436045
DOI: 10.4310/PAMQ.2010.V6.N4.A7
description: scientific article; zbMATH DE number 5904816