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Pseudo-Differential Operators with Symbols in Modulation Spaces

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Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 205))

Abstract

We establish continuity results for pseudo-differential operators with symbols in modulation spaces. Especially it follows from our general result that if a∈W ∞,1(R 2d), then the pseudo-differential operator a(x, D) is continuous from M ∞,1(R d) to W ∞,1(R d). If instead a∈W ∞,1(R 2d), then it follows that a(x, D) is continuous from M 1,∞(R d) to W 1,∞(R d).

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Author information

Authors and Affiliations

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

    Joachim Toft

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  1. Joachim Toft
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, 14469, Potsdam, Germany

    Bert-Wolfgang Schulze

  2. Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada

    M. W. Wong

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Toft, J. (2009). Pseudo-Differential Operators with Symbols in Modulation Spaces. In: Schulze, BW., Wong, M.W. (eds) Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations. Operator Theory: Advances and Applications, vol 205. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0198-6_13

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