Continuity properties in non-commutative convolution algebras, with applications in pseudo-differential calculus |
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Authors: | Joachim Toft |
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Affiliation: | Department of Mathematics, IHN, Blekinge Institute of Technology, S-371 79 Karlskrona, Sweden |
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Abstract: | We study continuity properties for a family {sp}p?1 of increasing Banach algebras under the twisted convolution, which also satisfies that a∈sp, 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 a∈s1 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. |
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Keywords: | 43Axx 47-XX 35S05 46-XX 42B35 42C99 16W80 |
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