Anisotropic pseudodifferential operators of type \(1,1\)
type: Item
instance of: scholarly article
title: Anisotropic pseudodifferential operators of type \(1,1\)
zbMATH Open document ID: 0955.35080
DOI: 10.1007/BF01759370
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2000-06-21T00:00:00Z
review text: This paper deals with several properties as boundedness and microlocal inclusion of a class of pseudodifferential operators (\(\psi\).d.o) of Hörmander's type 1,1 in the frame of anisotropic Sobolev spaces. The author introduces the anisotropic Littlewood-Paley decomposition and imposes some conditions on the symbols guaranteeing the continuity of the corresponding \(\psi\).d.o. in the anisotropic Sobolev spaces. The symbolic calculus developed in \S 3 enables the author to prove a ``sharp Gårding'' type inequality which includes the well-known Hörmander-Gårding inequality as well as its extension to anisotropic \(\psi\).d.o. proposed by Segala. Moreover, a microlocal inclusion for the wave-front sets of \(a(x,{\mathcal D})u\) and \(u\) of Sato type in the case of anisotropic Sobolev singularities is also shown.
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 47G30
zbMATH DE Number: 1463342
zbMATH Keywords: sharp Gårding type inequality
zbMATH Keywords: anisotropic Sobolev spaces
zbMATH Keywords: anisotropic Littlewood-Paley decomposition
zbMATH Keywords: wave-front sets
author: Gianluca Garello
reviewed by: Peter R. Popivanov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1463342