Continuity properties in non-commutative convolution algebras, with applications in pseudo-differential calculus
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文摘
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 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.
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 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.