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Subalgebras to a Wiener type Algebra of Pseudo-Differential operators
Blekinge Tekniska Högskola.ORCID iD: 0000-0003-1921-8168
2001 (English)In: Annales de l'Institut Fourier, ISSN 0373-0956, Vol. 51, no 5, 1347-1383 p.Article in journal (Refereed) Published
Abstract [en]

We study general continuity properties for an increasing family of Banach spaces $S^p_w$ of classes for pseudo-differential symbols, where $S^\infty_w=S_w$ was introduced by J. Sjöstrand in 1993. We prove that the operators in ${\rm Op}(S^p_w)$ are Schatten-von Neumann operators of order $p$ on $L^2$. We prove also that ${\rm Op}(S^p_w){\rm Op}(S^r_w)\subset {\rm Op}(S^r_w)$ and $S^p_w\cdot S^q_w\subset S^r_w$, provided $1/p + 1/q =1/r$. If instead $1/p +1/q = 1+1/r$, then $S^p_ww * S^q_w\subset S^r_w$. By modifying the definition of the $S^p_w$-spaces, one also obtains symbol classes related to the $S(m,g)$ spaces.

Place, publisher, year, edition, pages
Grenoble, 2001. Vol. 51, no 5, 1347-1383 p.
National Category
Mathematical Analysis
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-8508OAI: oai:DiVA.org:lnu-8508DiVA: diva2:352150
Projects
Matematisk modellering
Note
Vid tiden för publicering arbetade författaren vid Blekinge Tekniska HögskolaAvailable from: 2010-09-18 Created: 2010-09-18 Last updated: 2017-01-11Bibliographically approved

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