Melin-Hörmander inequality in a Wiener type pseudodifferential algebra
type: Item
instance of: scholarly article
title: Melin-Hörmander inequality in a Wiener type pseudodifferential algebra
zbMATH Open document ID: 1039.35149
DOI: 10.1007/BF02384559
published in: Arkiv för Matematik
publication date: 2004-03-28T00:00:00Z
review text: The main result of this paper is the proof of a Melin-Hörmander inequality for the Banach algebra of pseudo-differential operators associated to the class of symbols \(\Sigma ,\) consisting of elements \(a\in S^{\prime }(\mathbb{R}^{2n})\) such that \[ \sup_{Y\in \mathbb{R}^{2n}}\left| \widehat{\varphi _{Y}a}(X)\right| \in L^{1}(dX) , \] where \(\varphi \in S(\mathbb{R}^{2n})\backslash \left\{ 0\right\} ,\varphi _{Y}(\cdot )=\varphi (\cdot -Y)\) for \(Y\in \mathbb{R}^{2n},\) and \(\widehat{a} \) denotes the Fourier transform of \(a.\)
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 47L80
zbMATH DE Number: 2062424
zbMATH Keywords: Melin-Hörmander inequality
zbMATH Keywords: Banach algebra of pseudo-differential operators
zbMATH Keywords: symbols
author: F. Hérau
reviewed by: Chikh Bouzar
MaRDI profile type: Publication
cites work: Quantification asymptotique et microlocalisations d'ordre supérieur. I
cites work: Q4844851
cites work: Remarks on a Wiener type pseudodifferential algebra and Fourier integral operators
cites work: Lower bounds for pseudo-differential operators
cites work: An algebra of pseudodifferential operators
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description: scientific article; zbMATH DE number 2062424