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Continuity properties for non-commutative convolution algebras with applications in pseudo-differential calculus
Blekinge Tekniska Högskola.ORCID iD: 0000-0003-1921-8168
2002 (English)In: Bulletin des Sciences Mathématiques, ISSN 0007-4497, Vol. 126, no 2, 115-142 p.Article in journal (Refereed) Published
Abstract [en]

We study continuity properties for a family {sp}p1 of increasing Banach algebras under the twisted convolution, which also satisfies that asp, if and only if the Weyl operator aw(x,D) is a Schatten–von Neumann operator of order p on L2. We discuss inclusion relations between the sp-spaces, Besov spaces and Sobolev spaces. We prove also a Young type result on sp for dilated convolution. As an application we prove that f(a)s1, when as1 and f is an entire odd function. We finally apply the results on Toeplitz operators and prove that we may extend the definition for such operators.

Place, publisher, year, edition, pages
Elsevier , 2002. Vol. 126, no 2, 115-142 p.
National Category
Mathematical Analysis
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-8511DOI: 10.1016/S0007-4497(01)01089-2OAI: oai:DiVA.org:lnu-8511DiVA: diva2:352153
Projects
Matematisk modellering
Note
Vid tiden för publicering arbetade författaren vid Blekinge Tekniska Högskola.Available from: 2010-09-18 Created: 2010-09-18 Last updated: 2017-01-11Bibliographically approved

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CiteExportLink to record
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