Continuity properties for modulation spaces, with applications to pseudo-differential calculus. II
type: Item
instance of: scholarly article
title: Continuity properties for modulation spaces, with applications to pseudo-differential calculus. II
zbMATH Open document ID: 1098.47045
author: Joachim Toft
published in: Annals of Global Analysis and Geometry
publication date: 2004-08-20T00:00:00Z
review text: The author discusses general properties of pseudodifferential operators and Toeplitz operators in terms of weighted modulation spaces (MSs). The MS theory is extended in such a way that it might simplify applications of MSs to other fields, especially harmonic analysis. Basic properties of MSs are presented. It is shown that there is a canonical homeomorphism between MSs with different weight functions. In particular, the spaces \(M_s^{p,q}\) and \(M_{s,t}^{p,q}\) are constructed in a natural way from the standard space \(M^{p,q}\). This leads to embedding results between MSs and Sobolev/Besov spaces. By considering trace operators and extension operators in the background of MSs and using adjoint properties of these operators, one obtains some improvement in certain cases. From the above results, one obtains continuity results in operator theory for pseudodifferential operators and Toeplitz operators by making use of continuity properties of the ambiguity function in the context of MSs and relying on the role of this function in the Weyl calculus of pseudodifferential operators.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 2093690
zbMATH Keywords: modulation spaces
zbMATH Keywords: pseudodifferential operators
zbMATH Keywords: Toeplitz operators
zbMATH Keywords: trace theorem
zbMATH Keywords: embeddings
MaRDI profile type: Publication
Wikidata QID: Q115335118
full work available at URL: b:agag.0000023261.94488.f4
OpenAlex ID: W2044553252
DOI: 10.1023/B:AGAG.0000023261.94488.F4
description: scientific article; zbMATH DE number 2093690