Journal of Operator Theory

Volume 54, Issue 2, Fall 2005 pp. 387-399.

Modulation spaces and a class of bounded multilinear pseudodifferential operators

Authors: Arpad Benyi (1), Karlheinz Groechenig (2), Christopher Heil (3), and Kasso Okoudjou (4)
Author institution: (1) Department of Mathematics, 516 High St., Western Washington University, Bellingham, WA 098225--9063, USA, (2) Faculty of Mathematics, University of Vienna, Nordbergstr. 15, A-1090 Vienna, Austria, (3) School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332--0160, USA, (4) Department of Mathematics, Malott Hall, Cornell University, Ithaca, NY 14853--4201, USA

Summary: We show that multilinear pseudodifferential operators with symbols in the modulation space $\mathcal{M}(\infty,1)$ are bounded on products of modulation spaces. In particular, $\mathcal{M} (\infty,1)$ includes non-smooth symbols. Several multilinear Calder\'on--Vaillancourt-type theorems are then obtained by using certain embeddings of classical function spaces into modulation spaces.

Keywords: Modulation spaces, multilinear operators, pseudodifferential operators, short-time Fourier transform

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