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Modern Trends in Pseudo-Differential Operators pp 173–206Cite as

Continuity and Schatten Properties for Pseudo-differential Operators on Modulation Spaces

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 172))

Abstract

Let M p,q(ω) be the modulation space with parameters p, q and weight function ω. We prove that if t ∈ R, p, p j, q, q j ∈ [1, ∞], ω 1, ω 2 and ω are appropriate, and a ∈ M p,q(ω) , then the pseudo-differential operator a t(x,D) is continuous from M p1,q1(ω) to M p2,q2(ω) . If in addition p j = q j = 2, then we establish necessary and sufficient conditions on p and q in order to a t(x,D) should be a Schatten-von Neumann operator of certain order.

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  1. Department of Mathematics and Systems Engineering, Växjö University, Sweden

    Joachim Toft

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  1. Joachim Toft
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  1. School of Mathematics and Systems Engineering, Växjö University, SE-351 95, Växjö, Sweden

    Joachim Toft

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Toft, J. (2006). Continuity and Schatten Properties for Pseudo-differential Operators on Modulation Spaces. In: Toft, J. (eds) Modern Trends in Pseudo-Differential Operators. Operator Theory: Advances and Applications, vol 172. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8116-5_11

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